I think you kids have already realized that the teaching of reading, writing, and mathematics have fallen by the wayside, in favor of a pro Marxist agenda, where you were not taught critical thinking, but instead you were taught to assimilate a doctrine that will destroy the nation in which you live.
In high school, I aced algebra. In college, I aced calculus. But it's been over 50 years since those days and I've forgotten a LOT! Thanks for the review.
Same here About 45 years for me A lol though is coming back to me I could Take College Algebra again And could definitely do well And Take College level Trig at the same time I am going to audit Both of the classes this fall Being a senior citizen does has it’s advantages
Same here. I remembered that formula once I saw it. Good review. I have also been reviewing Trig and Calculus. I also want to study Geometry again. And Boolean Algebra. I have forgotten too much. This is fun.
You guys are so lucky I went to high school back in the seventies algebra was not a mandatory class.. I never had it I could have taken it I wish I did now I'm learning it at 61 it's harder at this age but I'm getting the hang of it slowly but surely
I have absolutely no use for quadratic equations at my age and in my situation, but you got me interested enough to look up the history of them. I do remember an algebra teacher that took up (wasted) one entire class period by showing on the blackboard how the quadratic equation was derived. Oh, I should mention that I found your presentation very clear and very useful.
I think it might be Bertrand Russell who said something similar to: "Education is the art of turning the obvious into something almost incomprehensible."
Your explanation is excelent. Wish I had you as a teacher at school. ( I'm 72 years old) I knew the quadratic formula but Imade so manny mistakes that the result was scrambled eggs in a tumbledryer.
12:32 you should stress, that you are looking for a number that can be square rooted, therefore not 2x6. In an Example such like a square root of 64, (2^2)(4^2) both can be square rooted and be 8^2, but 2x32 can not be squared for a full number. You should emphasize you're looking for a number that can be squared.
How many of your students understand what this quadratic equation represents and the relevance of this "answer", or more accurately in this case, these two answers? Without understanding what it is they are trying to solve for, do they realize the possibility of having two, one or even no solutions and why those possibilities exist? I found showing them visually what they are trying to solve for and what the possible results mean made for better understanding of the solutuons they end up with. I had them do a rough graph of their results. It made for a better overall grasp of what it is they're working with.
Not exactly a secret, it was first published by محمد بن موسى الخوارزمي Muḥammad ibn Musā al-Khwārazmi in the 9th century! We also get the word algebra from his book الكتاب المختصر في حساب الجبر والمقابلة al-Kitāb al-mukhtaṣar fī ḥisāb al-jabr w'al-muqābala. His Romanised name was Algorithmi from which we get the word algorithm.
I haven't seen this in 25 years and was quickly reminded of the formula. To this day, I have yet to find a use for this formula. Doing construction, many calculations are used involving algebra, geometry and some trigonometry, but nothing yet. Oh I remember the days of beating my head against the text book trying to understand. It's great when a coworker asks how much is 200mm and after a slight mental pause, respond with the answer is roughly 8" because they have to allow that much clearance for an electric fireplace. Checking on a conversion calculator, the answer is 7 7/8". That math is important also.
It all depends on your field. I use it all the time. The transfer function of a second order low pass filter is of the form: G(s)= 1/(as^2 + bs + c) The zeros of the denominator give the poles of the filter, and you need these to figure out what the values of L and C you need to implement the filter.
Hey, Erin, I also have never seen a use for quadratic equations. My teacher in ninth grade showed us how to do them with the “magic formula”, but never explained why, or what it was for. Ugh. I went all the way through Calculus and never had to use it again. I also don’t see why it is named Quadratic.
1/2.54=X/20, 2.54X=20, X=7.874. Converting .874 to a fraction is where I slowed down. When in school 70+years ago, I had a bunch of fractional/decimal equivalents memorized, but I was just now surprised to learn that I had forgotten 7/8. Well, I'm not going to bother relearning those things. I remember my 12 times tables, and that's enough. I also know Pi = 3.14/159/26/535/8979 (that's how I memorized them). I knew more, but I've forgotten them. Why did I learn past 3.14? Well, I read about this guy in "Ripley's Believe it or Not," so I wanted to see how I compared [NOT VERY WELL!!]
I took this in school, heard the other kids say why do we need this, the teacher said you will! I'm 57, a retired pilot, degree in Geological sciences, minor in math, never used this outside of school! Can't say that I ever saw this pop in day to day activity.
Just because you never used it doesn’t mean it’s not important. For anyone who wants to be an engineer or study physics or higher level math etc, understanding this formula is important for higher level mathematics.
@@JM-md4ri I get what you're saying, for higher level math, but is it necessary for the regular student that is not going to be an engineer, physicist, or whatever. I was just trying to point out that sometimes I think with all the other studies a student should learn, never do for subjects that may not be needed. I would venture that learning to wash and clean your clothes, is required more than these math concepts for 80% of the students. Not trying to offend, just a discussion.
More than half a lifetime ago, I was taking an Electronics II exam and I got myself into a Calc mess & tried to back out using a Fourier transform. Got to the point where I could use the Quadratic to solve. Then the professor put it up because another students asked for it. “I don’t know why you’d need this.” I let out an audible f-word. “Mr. Donovan, could you contain your Irish?” Math is hard.
y = a(x-h)² + k where h = 1/2(-b/a) and k = -a (h)² + c. a = 3, b = -6 and c = 2 so lets find h and k. h = 1/2(6/3), h = 1 k + -3(1)² + 2 = - 1 y = 3(x-1)² - 1. (prove it: 3(x - 1)(x-1) + 2. 3(x² - 2x + 1) - 1. does in fact give us 3x² - 6x + 2 solve for x x = h ± √(-k/a) x = 1 ± √(1/3) x = 1 ± √(3)/3 or as john shows it x = (3 ± √(3)/3). The 3 before the + or minus term is also divided by 3 so we can "pull it apart" so it is really 3/3 ± √(3)/3 bonus round the y intercept would be 2 the vertex of this parabola is the the set [1, -1] and the x intercepts are [1 + √(3)/3 and 1 - √(3)/3 ] I never could remember the clunky quadratic formula, but the vertex formula I could remember. Of course I only use it if I am sure the quadratic equation can't be solved by factoring.
I have a masters in engineering and to be honest I have never bothered with memorizing the quadratic formula. I find completing the square to be more intuitive and just as efficient as plugging all the values into the formula then reducing. Plus I never have to second guess my answer and whether I remembered the equation correctly when I haven’t used it in a while.
I prefer 1 +/- 1/sqrt(3). or 1 +/- sqrt(3)/3. And since everyone should know the decimal value of sort(3), 1.732... , you can get the decimal solution without a calculator in sight.
My math teacher tought me many years ago the next factoring: a2-a2 = a2-a2 (No mistake!) Left and right can be factored as follows a(a-a) = (a-a)(a+a) Then left and right can be devided by (a-a): a = (a+a) The brackets are useless now, so we can eleminate them: a = a+a Let’s simplificate that: a = 2a Deviding this by a gives: 1 = 2 With this riddle he wanted to illustrate a methematical taboo
Surely you should be starting with BOMDAS / BODMAS ie: Brackets, Of the Power, Multiplication, Division, Add and Subtract. Applying a formula before doing the above is overly complicated when it need not be.
NO! BODMAS only applies to people doing "sums". Algebra is mathematics and relying on BODMAS produces ambiguities and thus confusion. No user of mathematics would ever rely on BODMAS when writing a formula.
This is the standard presentation of the abc-formula. I have a better formula based on this one with a few steps that make you understand parabolas. My formula: x1,2 = xtop PLUS/MINUS delta With xtop = -b / 2a and delta = SQR (D) / 2a and D = b² - 4ac STEP 1 DISCRIMINANT First you work out the discriminant D = b² - 4ac When D > 0 then there are 2 points of the parabola crossing the x-axis When D = 0 then 1 point touching the x-axis (of course this is the top of the parabola) When D < 0 then there are no points crossing the x-axis, the parabola is fully above or under the x-axis In this case: D = (-6)² - 4.3.2 = 36 - 24 = 12 so there are 2 solutions for y = f(x) = 0 STEP 2 XTOP Now we know there are 2 solutions for y=0 we need to calculate the x-coordinate of the top of the parabola: xtop = -b / 2a This formula is part of the original abc-formula. The xtop is very important because the vertical line through xtop is the axis of symmetry of the parabola, so every point of the parabola has the same distance to this axis of symmetry. In this case: xtop = -(-6) / (2.3) = 6 / 6 = 1 STEP 3 DELTA This symmetry is also given for the crossings of the parabola with the x-axis, so the distance of x1 to xtop is the same as x2 to xtop The formula of this similar distance: delta = SQR(D) / 2a In this case: delta = SQR(12) / (2.3) = SQR(2.2.3) / 6 = SQR(3) / 3 STEP 4 SOLUTIONS FOR Y=0 The modified abc-formula: x1,2 = xtop PLUS/MINUS delta So x1 = xtop MINUS delta and x2 = xtop PLUS delta In this case: x1 = 1 MINUS SQR(3)/3 = 3/3 - SQR(3)/3 and x2 = 1 PLUS SQR(3)/3 = 3/3 + SQR(3)/3
As a teacher you might be interested in a slightly different approach to solving ANY simple quadratic. From the geometry of the quadratic we know that the curve is symmetrical about a vertical axis, let us say the line x = m. The roots R1 and R2 will be equidistant from this line. Without loss of generality we can assume R2>R1. The values R1 and R2 will be equidistant from the line x = m such that R1 = m - d. and R2 = m + d. By definition of what we mean by ' roots ' we can assert that (x - R1)*(x - R2 ) = 0 --> (x - (m - d))*( x - (m+d)) = 0 x^2 - (R1+R2)*x + R1*R2= 0 -> x^2 - (2*m)*x + (m-d)*(m+d) -> x^2 - 2*m*x + (m^2-d^2) referring back to the general equation a*x^2 + b*x + c = 0 m=-- 2*b/a and d = sqrt (m^2 -c/a ) R1 := -2*b/a - sqrt((4*b^2/a^2)-c/a) and R2 = -2*b/a + sqrt((4*b^2/a^2)-c/a) The last line is complicated so in practice it's easier to remember the previous line expressing m and d. Of course there will always be students who prefer to learn things by rote, and will not concern themselves with proofs. For the more serious student, I think this is a simple one to follow and my private opinion is that the expressions for m and d are simple enough to remember.
@@digitalkittycat4274 He really gets enthusiastic. But I wonder why when explaining a basic proof in algebra, he does not use algebra, and insists on demonstrating specific cases. I'm wondering what audience he's addressing.
@@crustyoldfart I am not a judge, but ........ I guess he wants to prove. To prove you need "facts with evidence". I guess examples are the evidence. so he proves the fact (theory/algebra) with examples. :-) You are correct. He should have used algebraic proof in addition !!
Why don’t any courses in U.K. or USA teach math about finances, savings, credit cards, stock market investments, APR, inflation and so on. These are life skills that I only realised in my 30s!
@@NacGT4 When u have people in their 20’s asking their parents how to do it, it’s not taught. The problem is parents don’t always know how to do it either. Merry Christmas!
Where did you get the ax squared plus bx plus c = 0 thing from? We were at the quadratic then you started using that one what’s that and when do I know to use it?
Why is a quadratic formula import? Tell me where I would use it? I left school 60 years ago, trained as an electrical engineer and have never seen an application for it. I have asked other engineers and get, yes I remember that but no idea where you would need it.
I literally don't even know how I got an A in Algebra when this seems so foreign to me. I don't remember any of it. I would literally need to start in Pre-Algebra again and work my way back to here.
I'm going to be 70 years old on New Years day and remember this formula very well from my school days in the UK. I have just one question, I cannot remember why (-6) squared is = 36 and not (-36)
I have never heard a “logical “explanation, it was just a rule…. Plus x plus = plus; plus x minus = minus ; minus x minus = plus………sort of like a double negative in language……”I can’t not do it” means I can do it.
(-6)² couldn't be -36 because 6x(-6)=(-36) and 6x(-6) can't be the same as (-6)x(-6); but basically, yes, you just have to accept that negative x negative = positive. [And I beat you just: I'm already 70 LOL]
Think of the (-) as meaning "reverse the sign." If you have a positive number 6 and reverse the sign you get (-6). This is (-1)*6. Reverse the sign again and you get 6. This is (-1)*(-1)*6 = 6. So if you reverse the sign an even number of times the sign is unchanged. If you reverse it an odd number of times the sign is changed. So (-6)*(-6) = 36 -- the sign has been reversed twice. (-6)^3 = -216 because the sign has been changed three times, from positive to negative to positive. And so on. It is entirely logical and you do not have to just accept it, but you can reason it out. A useful way to see this is by using a number line, and there will be lots of videos doing this.
Plse you have to remember that the polarities multiplied can change Example: - × - = + - × + = - + × - = - + × + = + That is why the polarities are so important to remember thanks
Ok I remember how to do this Though I almost made mist mistake as My Algebra 1 Teacher would say “Watch your signs “ I got a little too over confident But I caught it ..Doing Math is a progression You build on what you have already learned As you progress you will have yo previously learn to do the next problems Simply stated you need the skills you learned in Algebra 1 to be able to do Algebra 2 You will need those skills to do Trig Once you have mastered those skills comes Pre - Calculus or Calculus 1 And you used all those Skills to do A lot More Calculus So you take all those above mention math Classes…You need them to do Calculus…With Calculus The door is open the sky is the limit
I've always remembered that formula from 44 years since I had to use it. And although I've used many parts of maths again in my life, it's never once even remotely been useful. And to be honest, once I'd gotten square root of 12, I can't see any gain from reducing it further, since either way you'd be reaching for the calculator.
Mainly because a calculator cannot tell you the value of √12 [or √3] - it can only give an approximation. The aim is simplification; the same reason we reduce 4/6 to 2/3.
wish you'd explain mathematically why can't factor when numerator has addition or subtraction (as opposed to multiplication or division). You didn't really explain it in your video noting one can't factor in that case.
This may sound like a stupid question but exactly how do you know to plug in the a-b-c values for the numbers in the original equation? 5:22. Why A squared? why not B squared since B is squared in the Quadratic equation.
Do you mean by A squared is that ax² ?? So if that, ax²+bx+c = 0, where a, b and c only replace coefficients or constant. In Quadratic Equation, 'c' is the constant because it is the term that has no "x". The 'a' is simply the leading coefficient of the polynomial. In Cubic Equation, we have ax³+bx²+cx+d = 0 where 'a' is still the leading coefficient while 'd' is the constant. On the other hand, that b² inside the radical is not as same as a² or ax² that you may be talking about. √b² - 4ac is called discriminant. It is just a part of the Quadratic Formula itself. Should be noted also that Cubic, Quartic, Quintic..... Equations do not have this.
Hello everyone, In addition to the completing the square that I used in my first posting and the abc formula from the video (which I used in my second posting), the pq formula can also be used to solve this quadratic equation. It would then go like this: 3x² - 6x + 2 = 0 | ‧ ⅓ x² - 2x + ⅔ = 0 ------ x₁ / x₂ = -(p/2) ± √((p/2)² - q) p = -2 q = ⅔ ------ x₁ = -((-2)/2) + √(((-(2/2))² - ⅔) x₁ = 1 + √((-1)² - ⅔) x₁ = 1 + √(1 - ⅔) x₁ = 1 + √(⅓) x₂ = 1 - √(⅓) Best regards Marcus 😎
When I taught Alg 1 thirty some years ago, I required my students to be able to derive the quadratic formula as a formal proof before they could receive their final grade. The most awful crying and moaning and gnashing of teeth imaginable. The students I ran into later in their life thanked me because the confidence they gained allowed them to attempt higher level math courses in college. You're welcome guys!
I think you should have also mentioned 'Completing the square as a solution', particularly as this is how the quadratic formula was originally derived! In fact, do this to get the solution - very easy. I would also have written the answer as: x = 1 ± 1/√3, which is a very tidy way of expressing it.
@@markdavis9990 My suggestion was perfectly legitimate - any student learning about the quadratic formula should be made aware how it was derived. You're welcome to express your opinion, but my comment was made with the best of intentions. I would hope your comment was meant as a jocular response.
I got the same answer by completing the square: x = 1 ± 1/√3 which simplifies to 1 ± √3/3 (I think). Is this the same value as the above answer: 3 ± √3/3 produced from the quadratic formula? Can 3 ± √3/3 be simplified further like what one gets by completing the square?
Having an engineering background I would agree . However, 'proper' mathematicians don't like surds (√3) in the denominator (as I have learned teaching higher level mathematics for the past 30 years). I also agree with some of the comments that the completing the square method should be shown to be complete. Having said all that any help to increase student's confidence and competence in what they perceive as the difficult parts is to be congratulated. Well done sir.
Just to jump in, the word "secret" isn't appropriately pedagogical when it comes to mathematics, since there's no secret in mathematics. Math is all about understanding.
a formula without developing it is criminal. You should use krafts to develope the formula. So get out your paper , glue and scissors. Rearrange the standard form quadratic . First make a =1 by dividing all terms by a . We get x^2+(b/a)x +c/a = 0/a=0 The c/a term is a number. Subtract it from both sides of the equation. To get X^2+ (b/a)x = -c/a The left side of the equation consists of a square (x) by (x) and a rect. X by (b/a). Get the scissors out and cut the rectangle lengthwise into 2 equal parts. Now we have a square and 2 rect. (X by b/(2a)) Glue the 2 rectangles to each side of the square. We now have a square x+b/(2a) by x + b/(2a) Area =(X +b/(2a))^2 Well almost. We have overstated by b/(2a) by b/(2a) Area =((b/(2a))^2 We now have a square and an anti square on the left side. The anti square is a number so by adding to both sides of the equation The left side of the equation is a square and the right side is number solve for x in terms of a,b, c you get X= (-b +- (b^2 - 4ac)^1/2)/2a By completing the square.
I can live with the usual interruption when you ask your viewers to subscribe but the adds are really a pain in the quadratic formula, if you get my drift. You should give your viewers a break from commercials once in a while.
Sorry John but did you say that you have a huge LIBARY or LIBRARY. If you said Library, then I would suggest checking on your English grammar and pronunciation notes.
This guy used a box of tools, twenty jackhammers, a gallon of marbles, 14 human sacrifices, and a note from his mother to calculate the “2” that all of us could see in about three seconds.
I appreciate your effort in trying to help students with math - it is so important that all students know that you don't have to be special to do well in math. That being said, I am disappointed that the cornerstone of your lesson is to encourage students to memorize a formula. (It takes very little effort to plug numbers into a formula and it is not very rewarding.) This is absolutely the most destructive approach to learning math and one that turns otherwise intelligent students away from science in general. For god sake, teach them how to develop the quadratic formula. It's basic and any reasonably intelligent student can learn it in short order. Math isn't about blindly memorizing formulas on faith.
2 mistakes in this video. He said a was a variable. In fact a is a constant in this problem. More importantly he failed to point out that a, b & c are coefficients...
Are you trying to help or just show how smart you are,you could have slowed down just a bit for those that are not as knowledgeable as you are, for I was very eager to get this but you lost me at the square root of 12, could have explained that part little more indept ,after that I lost my will in frustration to anger to carry on,thanks for getting my hopes up to being more intelligent in mathematical equations only to feel less than .
This is all about the so-called abc-formula, very easy when you cannot factor a quadratic equation. It also contains the so-called Discriminant (b^2 - 4ac), which informs you about the 'fractionability' of a quadratic equation (if the D = 0 you can always fraction the equation) and about the kind of the solution ( 2 real numbers, one 'double' solution or also imaginary numbers as solution(s) ).
The Quadratic Formula: To the tune of Row Row Row your Boat: x equals minus b, plus or minus the square root of b squared minus four a c, all over two a.
Great experience, thank you, it can help with heaps of students who do not understand in equations like this! Thank you once again. God bless your online class,
I’m an 8th grader doing pre algebra and I decided I’m going to teach myself algebra and calculus since the school doesn’t want to
Quite right, go for it, then study classical mechanics!
7th Grader and still here
Get it son! Don’t stop after differential/integral calculus. Multivariable/vector calculus is the coolest
Nahh im a 6th grader 💀💀💀💀
I think you kids have already realized that the teaching of reading, writing, and mathematics have fallen by the wayside, in favor of a pro Marxist agenda, where you were not taught critical thinking, but instead you were taught to assimilate a doctrine that will destroy the nation in which you live.
In high school, I aced algebra. In college, I aced calculus. But it's been over 50 years since those days and I've forgotten a LOT! Thanks for the review.
Same here About 45 years for me A lol though is coming back to me I could Take College Algebra again And could definitely do well And Take College level Trig at the same time I am going to audit Both of the classes this fall Being a senior citizen does has it’s advantages
I was going to call you a show-off but you redeemed yourself with the end of your comment. 😊
Same here. I remembered that formula once I saw it. Good review. I have also been reviewing Trig and Calculus. I also want to study Geometry again. And Boolean Algebra. I have forgotten too much.
This is fun.
Me, too. I had a lot of college math, ending with Advanced Enginering Math (DE), but now I have also forgotten almost all of it. Ouch.
You guys are so lucky I went to high school back in the seventies algebra was not a mandatory class.. I never had it I could have taken it I wish I did now I'm learning it at 61 it's harder at this age but I'm getting the hang of it slowly but surely
I was utterly lost 40 years ago when I was trying to learn this. Nothing has changed.
I have absolutely no use for quadratic equations at my age and in my situation, but you got me interested enough to look up the history of them. I do remember an algebra teacher that took up (wasted) one entire class period by showing on the blackboard how the quadratic equation was derived. Oh, I should mention that I found your presentation very clear and very useful.
I think it might be Bertrand Russell who said something similar to: "Education is the art of turning the obvious into something almost incomprehensible."
Your explanation is excelent. Wish I had you as a teacher at school. ( I'm 72 years old) I knew the quadratic formula but Imade so manny mistakes that the result was scrambled eggs in a tumbledryer.
Maybe you just weren’t paying attention.
@@Willowdog08 😂😂😂🤦🏽
12:32 you should stress, that you are looking for a number that can be square rooted, therefore not 2x6. In an Example such like a square root of 64, (2^2)(4^2) both can be square rooted and be 8^2, but 2x32 can not be squared for a full number. You should emphasize you're looking for a number that can be squared.
How many of your students understand what this quadratic equation represents and the relevance of this "answer", or more accurately in this case, these two answers? Without understanding what it is they are trying to solve for, do they realize the possibility of having two, one or even no solutions and why those possibilities exist? I found showing them visually what they are trying to solve for and what the possible results mean made for better understanding of the solutuons they end up with. I had them do a rough graph of their results. It made for a better overall grasp of what it is they're working with.
Thanks....it's fun to get back into algebra..... it's been 50 years for me.
Excellent teacher/instructor. 😊
Not exactly a secret, it was first published by محمد بن موسى الخوارزمي Muḥammad ibn Musā al-Khwārazmi in the 9th century! We also get the word algebra from his book الكتاب المختصر في حساب الجبر والمقابلة al-Kitāb al-mukhtaṣar fī ḥisāb al-jabr w'al-muqābala. His Romanised name was Algorithmi from which we get the word algorithm.
I haven't seen this in 25 years and was quickly reminded of the formula. To this day, I have yet to find a use for this formula. Doing construction, many calculations are used involving algebra, geometry and some trigonometry, but nothing yet. Oh I remember the days of beating my head against the text book trying to understand.
It's great when a coworker asks how much is 200mm and after a slight mental pause, respond with the answer is roughly 8" because they have to allow that much clearance for an electric fireplace. Checking on a conversion calculator, the answer is 7 7/8". That math is important also.
It all depends on your field. I use it all the time. The transfer function of a second order low pass filter is of the form: G(s)= 1/(as^2 + bs + c) The zeros of the denominator give the poles of the filter, and you need these to figure out what the values of L and C you need to implement the filter.
Hey, Erin, I also have never seen a use for quadratic equations. My teacher in ninth grade showed us how to do them with the “magic formula”, but never explained why, or what it was for. Ugh. I went all the way through Calculus and never had to use it again. I also don’t see why it is named Quadratic.
1/2.54=X/20, 2.54X=20, X=7.874. Converting .874 to a fraction is where I slowed down. When in school 70+years ago, I had a bunch of fractional/decimal equivalents memorized, but I was just now surprised to learn that I had forgotten 7/8. Well, I'm not going to bother relearning those things. I remember my 12 times tables, and that's enough. I also know Pi = 3.14/159/26/535/8979 (that's how I memorized them). I knew more, but I've forgotten them. Why did I learn past 3.14? Well, I read about this guy in "Ripley's Believe it or Not," so I wanted to see how I compared [NOT VERY WELL!!]
I took this in school, heard the other kids say why do we need this, the teacher said you will! I'm 57, a retired pilot, degree in Geological sciences, minor in math, never used this outside of school! Can't say that I ever saw this pop in day to day activity.
Just because you never used it doesn’t mean it’s not important. For anyone who wants to be an engineer or study physics or higher level math etc, understanding this formula is important for higher level mathematics.
@@JM-md4ri I get what you're saying, for higher level math, but is it necessary for the regular student that is not going to be an engineer, physicist, or whatever. I was just trying to point out that sometimes I think with all the other studies a student should learn, never do for subjects that may not be needed. I would venture that learning to wash and clean your clothes, is required more than these math concepts for 80% of the students. Not trying to offend, just a discussion.
More than half a lifetime ago, I was taking an Electronics II exam and I got myself into a Calc mess & tried to back out using a Fourier transform. Got to the point where I could use the Quadratic to solve. Then the professor put it up because another students asked for it. “I don’t know why you’d need this.” I let out an audible f-word.
“Mr. Donovan, could you contain your Irish?”
Math is hard.
Thank you so much. I really appreciate you helping me understand this formula! :)
Confused as hell 😂🤣😂🤣. Definitely have to rewatch.
the quadratic formula is good to know but this example is easily solved using complete the square.
Great video. I needed the refresher.
y = a(x-h)² + k where h = 1/2(-b/a) and k = -a (h)² + c. a = 3, b = -6 and c = 2 so lets find h and k.
h = 1/2(6/3), h = 1
k + -3(1)² + 2 = - 1
y = 3(x-1)² - 1. (prove it: 3(x - 1)(x-1) + 2. 3(x² - 2x + 1) - 1. does in fact give us 3x² - 6x + 2
solve for x
x = h ± √(-k/a)
x = 1 ± √(1/3)
x = 1 ± √(3)/3 or as john shows it x = (3 ± √(3)/3). The 3 before the + or minus term is also divided by 3 so we can "pull it apart" so it is really 3/3 ± √(3)/3
bonus round
the y intercept would be 2
the vertex of this parabola is the the set [1, -1]
and the x intercepts are [1 + √(3)/3 and 1 - √(3)/3 ]
I never could remember the clunky quadratic formula, but the vertex formula I could remember. Of course I only use it if I am sure the quadratic equation can't be solved by factoring.
I have a masters in engineering and to be honest I have never bothered with memorizing the quadratic formula. I find completing the square to be more intuitive and just as efficient as plugging all the values into the formula then reducing. Plus I never have to second guess my answer and whether I remembered the equation correctly when I haven’t used it in a while.
Completing the square does not work well when the two roots include square roots, as it does here.
You said put that into your long term memory. I'm 68 and STILL know it despite never using it since school. Will that do?
That’s brilliant to revisit quadratic equations. Can it be solved in this way?
(3X-2)x(X-1) that way solution is x=1 or 2/3
The quadratic formula can be derived by using the completing the square strategy.
I prefer 1 +/- 1/sqrt(3). or 1 +/- sqrt(3)/3. And since everyone should know the decimal value of sort(3), 1.732... , you can get the decimal solution without a calculator in sight.
Yes I didn’t like how he didn’t factor out the 3
Right!? I'm goijg why, why is he claiming we canr factor this, it makes no sense we wouldn't leave it in lowest terms!
My math teacher tought me many years ago the next factoring:
a2-a2 = a2-a2 (No mistake!)
Left and right can be factored as follows
a(a-a) = (a-a)(a+a)
Then left and right can be devided by (a-a):
a = (a+a)
The brackets are useless now, so we can eleminate them:
a = a+a
Let’s simplificate that:
a = 2a
Deviding this by a gives:
1 = 2
With this riddle he wanted to illustrate a methematical taboo
Lol
MR. TabletClass Math thank you for a fantastic video.
Surely you should be starting with BOMDAS / BODMAS ie: Brackets, Of the Power, Multiplication, Division, Add and Subtract. Applying a formula before doing the above is overly complicated when it need not be.
NO! BODMAS only applies to people doing "sums". Algebra is mathematics and relying on BODMAS produces ambiguities and thus confusion. No user of mathematics would ever rely on BODMAS when writing a formula.
Good review after 20-40 years, trying to help granddaughter
😊
You could just derive the equation by completing the square.
...on the standard form of a quadratic equation.
Bro no way, I am thrilled to try this for first time in 24 years of my life.
Good evening, genius sir, working out this sum
Ans,x=(6+✓60)/6,(6-✓60)/6
This is the standard presentation of the abc-formula. I have a better formula based on this one with a few steps that make you understand parabolas.
My formula: x1,2 = xtop PLUS/MINUS delta
With xtop = -b / 2a and delta = SQR (D) / 2a and D = b² - 4ac
STEP 1 DISCRIMINANT
First you work out the discriminant D = b² - 4ac
When D > 0 then there are 2 points of the parabola crossing the x-axis
When D = 0 then 1 point touching the x-axis (of course this is the top of the parabola)
When D < 0 then there are no points crossing the x-axis, the parabola is fully above or under the x-axis
In this case: D = (-6)² - 4.3.2 = 36 - 24 = 12 so there are 2 solutions for y = f(x) = 0
STEP 2 XTOP
Now we know there are 2 solutions for y=0 we need to calculate the x-coordinate of the top of the parabola: xtop = -b / 2a
This formula is part of the original abc-formula.
The xtop is very important because the vertical line through xtop is the axis of symmetry of the parabola, so every point of the parabola has the same distance to this axis of symmetry.
In this case: xtop = -(-6) / (2.3) = 6 / 6 = 1
STEP 3 DELTA
This symmetry is also given for the crossings of the parabola with the x-axis, so the distance of x1 to xtop is the same as x2 to xtop
The formula of this similar distance: delta = SQR(D) / 2a
In this case: delta = SQR(12) / (2.3) = SQR(2.2.3) / 6 = SQR(3) / 3
STEP 4 SOLUTIONS FOR Y=0
The modified abc-formula: x1,2 = xtop PLUS/MINUS delta
So x1 = xtop MINUS delta and x2 = xtop PLUS delta
In this case: x1 = 1 MINUS SQR(3)/3 = 3/3 - SQR(3)/3 and x2 = 1 PLUS SQR(3)/3 = 3/3 + SQR(3)/3
we just learnt this a week ago 😅
This is quadràtic equation..x= plus/minus the square root of b squared minus 4ac all over 2a.
As a teacher you might be interested in a slightly different approach to solving ANY simple quadratic.
From the geometry of the quadratic we know that the curve is symmetrical about a vertical axis, let us say the line x = m. The roots R1 and R2 will be equidistant from this line. Without loss of generality we can assume R2>R1. The values R1 and R2 will be equidistant from the line x = m such that
R1 = m - d. and R2 = m + d.
By definition of what we mean by ' roots ' we can assert that
(x - R1)*(x - R2 ) = 0 --> (x - (m - d))*( x - (m+d)) = 0
x^2 - (R1+R2)*x + R1*R2= 0 -> x^2 - (2*m)*x + (m-d)*(m+d) -> x^2 - 2*m*x + (m^2-d^2)
referring back to the general equation a*x^2 + b*x + c = 0
m=-- 2*b/a and d = sqrt (m^2 -c/a )
R1 := -2*b/a - sqrt((4*b^2/a^2)-c/a) and R2 = -2*b/a + sqrt((4*b^2/a^2)-c/a)
The last line is complicated so in practice it's easier to remember the previous line expressing m and d.
Of course there will always be students who prefer to learn things by rote, and will not concern themselves with proofs. For the more serious student, I think this is a simple one to follow and my private opinion is that the expressions for m and d are simple enough to remember.
Excellent !
@@digitalkittycat4274 Glad you liked this approach. I take it you agree it's simpler to remember m and d ?
@@crustyoldfart There is an explanation video by Dr. Peyam, that fits I think.
ua-cam.com/video/WRl0SRSF3BU/v-deo.html
@@digitalkittycat4274 He really gets enthusiastic. But I wonder why when explaining a basic proof in algebra, he does not use algebra, and insists on demonstrating specific cases. I'm wondering what audience he's addressing.
@@crustyoldfart I am not a judge, but ........
I guess he wants to prove. To prove you need "facts with evidence". I guess examples are the evidence. so he proves the fact (theory/algebra) with examples. :-)
You are correct. He should have used algebraic proof in addition !!
Why don’t any courses in U.K. or USA teach math about finances, savings, credit cards, stock market investments, APR, inflation and so on. These are life skills that I only realised in my 30s!
I live in Canada and it's taught in grade 12.
Because these are not Mathematics, they are Economics.
@@NacGT4 It doesn't matter what it's classfied as, it should be taught.
@@liamwelsh5565 My point is that they are taught! You just have to realise the applicable skills that you know!
@@NacGT4 When u have people in their 20’s asking their parents how to do it, it’s not taught. The problem is parents don’t always know how to do it either. Merry Christmas!
No need for any so-called secret formula:
3x^2 - 6x + 2 = 0
3x^2 - 6x + 3 - 1 = 0
3 * ( x^2 - 2x + 1 ) - 1 = 0
3 * ( x - 1 )^2 - 1 = 0
( x - 1 )^2 = 1 / 3
x - 1 = + or - sqrt ( 1 / 3 )
x = 1 + or - sqrt ( 1 / 3 )
Very clear
Binomial eqn. Pentagorias theorem .
there is a factor to take into account.
Where did you get the ax squared plus bx plus c = 0 thing from? We were at the quadratic then you started using that one what’s that and when do I know to use it?
You’re the boss my 🎩 thank you 😊
Thank you 😊💓
Why is a quadratic formula import? Tell me where I would use it? I left school 60 years ago, trained as an electrical engineer and have never seen an application for it. I have asked other engineers and get, yes I remember that but no idea where you would need it.
I literally don't even know how I got an A in Algebra when this seems so foreign to me. I don't remember any of it. I would literally need to start in Pre-Algebra again and work my way back to here.
And I got the pleasure, Pleiades, The Tri Days, Steps, De Mond, we don't put an E
I'm going to be 70 years old on New Years day and remember this formula very well from my school days in the UK. I have just one question, I cannot remember why (-6) squared is = 36 and not (-36)
I have never heard a “logical “explanation, it was just a rule…. Plus x plus = plus; plus x minus = minus ; minus x minus = plus………sort of like a double negative in language……”I can’t not do it” means I can do it.
(-6)² couldn't be -36 because 6x(-6)=(-36) and 6x(-6) can't be the same as (-6)x(-6); but basically, yes, you just have to accept that negative x negative = positive. [And I beat you just: I'm already 70 LOL]
a negative number squared results in a positive result, hence -6^2= (6-) x (-6) = +36
Think of the (-) as meaning "reverse the sign." If you have a positive number 6 and reverse the sign you get (-6). This is (-1)*6. Reverse the sign again and you get 6. This is (-1)*(-1)*6 = 6. So if you reverse the sign an even number of times the sign is unchanged. If you reverse it an odd number of times the sign is changed. So (-6)*(-6) = 36 -- the sign has been reversed twice. (-6)^3 = -216 because the sign has been changed three times, from positive to negative to positive. And so on. It is entirely logical and you do not have to just accept it, but you can reason it out. A useful way to see this is by using a number line, and there will be lots of videos doing this.
Plse you have to remember that the polarities multiplied can change
Example: - × - = +
- × + = -
+ × - = -
+ × + = +
That is why the polarities are so important to remember
thanks
Actually, you can go a step further by separating this "final answer" into (3/3)±(√3/3) = 1±(√3/3). This is your true final answer.
Ok I remember how to do this Though I almost made mist mistake as My Algebra 1 Teacher would say “Watch your signs “ I got a little too over confident But I caught it ..Doing Math is a progression You build on what you have already learned As you progress you will have yo previously learn to do the next problems Simply stated you need the skills you learned in Algebra 1 to be able to do Algebra 2 You will need those skills to do Trig Once you have mastered those skills comes Pre - Calculus or Calculus 1 And you used all those Skills to do A lot More Calculus So you take all those above mention math Classes…You need them to do Calculus…With Calculus The door is open the sky is the limit
I've always remembered that formula from 44 years since I had to use it. And although I've used many parts of maths again in my life, it's never once even remotely been useful. And to be honest, once I'd gotten square root of 12, I can't see any gain from reducing it further, since either way you'd be reaching for the calculator.
Mainly because a calculator cannot tell you the value of √12 [or √3] - it can only give an approximation. The aim is simplification; the same reason we reduce 4/6 to 2/3.
wish you'd explain mathematically why can't factor when numerator has addition or subtraction (as opposed to multiplication or division). You didn't really explain it in your video noting one can't factor in that case.
The Quadratic formula or factoring
This may sound like a stupid question but exactly how do you know to plug in the a-b-c values for the numbers in the original equation? 5:22. Why A squared? why not B squared since B is squared in the Quadratic equation.
Do you mean by A squared is that ax² ?? So if that, ax²+bx+c = 0, where a, b and c only replace coefficients or constant. In Quadratic Equation, 'c' is the constant because it is the term that has no "x". The 'a' is simply the leading coefficient of the polynomial.
In Cubic Equation, we have ax³+bx²+cx+d = 0 where 'a' is still the leading coefficient while 'd' is the constant.
On the other hand, that b² inside the radical is not as same as a² or ax² that you may be talking about.
√b² - 4ac is called discriminant. It is just a part of the Quadratic Formula itself. Should be noted also that Cubic, Quartic, Quintic..... Equations do not have this.
Quadratic equation or completing a square.
Ok ..I got 1 +/- 3 to the -3rd power .. But is that wrong?
Hello everyone,
In addition to the completing the square that I used in my first posting and the abc formula from the video (which I used in my second posting), the pq formula can also be used to solve this quadratic equation. It would then go like this:
3x² - 6x + 2 = 0 | ‧ ⅓
x² - 2x + ⅔ = 0
------
x₁ / x₂ = -(p/2) ± √((p/2)² - q)
p = -2
q = ⅔
------
x₁ = -((-2)/2) + √(((-(2/2))² - ⅔)
x₁ = 1 + √((-1)² - ⅔)
x₁ = 1 + √(1 - ⅔)
x₁ = 1 + √(⅓)
x₂ = 1 - √(⅓)
Best regards
Marcus 😎
When I taught Alg 1 thirty some years ago, I required my students to be able to derive the quadratic formula as a formal proof before they could receive their final grade. The most awful crying and moaning and gnashing of teeth imaginable. The students I ran into later in their life thanked me because the confidence they gained allowed them to attempt higher level math courses in college.
You're welcome guys!
Shouldn't the PURPOSE of this ANSWER be illustrated in some form or fashion? I don't understand the ANSWER.
It’s not a secret formula it’s one of the basic high school u learn at your first lesson
I think you should have also mentioned 'Completing the square as a solution', particularly as this is how the quadratic formula was originally derived! In fact, do this to get the solution - very easy.
I would also have written the answer as: x = 1 ± 1/√3, which is a very tidy way of expressing it.
No one likes a “smart ass”!
@@markdavis9990 My suggestion was perfectly legitimate - any student learning about the quadratic formula should be made aware how it was derived. You're welcome to express your opinion, but my comment was made with the best of intentions. I would hope your comment was meant as a jocular response.
I got the same answer by completing the square: x = 1 ± 1/√3 which simplifies to 1 ± √3/3 (I think). Is this the same value as the above answer: 3 ± √3/3 produced from the quadratic formula? Can 3 ± √3/3 be simplified further like what one gets by completing the square?
Having an engineering background I would agree . However, 'proper' mathematicians don't like surds (√3) in the denominator (as I have learned teaching higher level mathematics for the past 30 years). I also agree with some of the comments that the completing the square method should be shown to be complete. Having said all that any help to increase student's confidence and competence in what they perceive as the difficult parts is to be congratulated. Well done sir.
@@dhulem ...and you're surprised that you got the same answer???
Just to jump in, the word "secret" isn't appropriately pedagogical when it comes to mathematics, since there's no secret in mathematics. Math is all about understanding.
Why exactly cant we do 1+/- sqrt(3)/3?
I just need numbers to play this game.
If it takes 17 minutes to solve one problem..... I flunked already.
a formula without developing it is criminal.
You should use krafts to develope the formula. So get out your paper , glue and scissors.
Rearrange the standard form quadratic . First make a =1 by dividing all terms by a . We get x^2+(b/a)x +c/a = 0/a=0
The c/a term is a number. Subtract it from both sides of the equation. To get
X^2+ (b/a)x = -c/a
The left side of the equation consists of a square (x) by (x) and a rect.
X by (b/a). Get the scissors out and cut the rectangle lengthwise into 2 equal parts.
Now we have a square and 2 rect. (X by b/(2a))
Glue the 2 rectangles to each side of the square.
We now have a square x+b/(2a) by x + b/(2a)
Area =(X +b/(2a))^2
Well almost. We have overstated by b/(2a) by
b/(2a)
Area =((b/(2a))^2
We now have a square and an anti square on the left side. The anti square is a number so by adding to both sides of the equation
The left side of the equation is a square and the right side is number solve for x in terms of
a,b, c you get
X= (-b +- (b^2 - 4ac)^1/2)/2a
By completing the square.
15:05 can’t u simplify the 3’s to just leave +- the square root of 3 as an answer?
No; do the math
That is abc formula only when the D is < 0,
I was thinking you might derive the quadratic formula by demonstration of completing the square…
I can live with the usual interruption when you ask your viewers to subscribe but the adds are really a pain in the quadratic formula, if you get my drift.
You should give your viewers a break from commercials once in a while.
Quadratic?
Where's the secret ?
Uh...
Man you're ok ?
Move it along.
Sorry John but did you say that you have a huge LIBARY or LIBRARY. If you said Library, then I would suggest checking on your English grammar and pronunciation notes.
This guy used a box of tools, twenty jackhammers, a gallon of marbles, 14 human sacrifices, and a note from his mother to calculate the “2” that all of us could see in about three seconds.
And I thought he used a formula.
a = 3
b = -6
c = 2
I appreciate your effort in trying to help students with math - it is so important that all students know that you don't have to be special to do well in math. That being said, I am disappointed that the cornerstone of your lesson is to encourage students to memorize a formula. (It takes very little effort to plug numbers into a formula and it is not very rewarding.) This is absolutely the most destructive approach to learning math and one that turns otherwise intelligent students away from science in general. For god sake, teach them how to develop the quadratic formula. It's basic and any reasonably intelligent student can learn it in short order. Math isn't about blindly memorizing formulas on faith.
No, not the quadratic formula! Anything but that>!!
Answer is 2
A + B + C=?
A++B+C=
3----6++2==
------3++2==----1
It is the formula to solve quadratic equation .for. A 9th class student
Not any secret
This is not any secret formula, it is taught in tenth standerd in India, (SSC Board
You have a huge libary? Does your libary, per chance, contain any library books?
Nose bleed,so many solution..is there any short cut sir🤣🤣👍👍👍
2 mistakes in this video. He said a was a variable. In fact a is a constant in this problem. More importantly he failed to point out that a, b & c are coefficients...
Your approach is much too slow, repetitious, very tedious, and not necessary.
Well, ...
Didn’t like it because of no check answer and no explanation .
On behalf of math tutors everywhere, I thank you for this explanation and ask forgiveness for all the rude comments from “experts.”
shhhhh, it's a secret! Don't tell us!!
Not really. If you give me the formula then would it be still a secret formula.
This is simple quadratic equation he is taking 17 mins to solve thr problem
Complicated
You talk too much. Just get to the problem.
💖✨
Are you trying to help or just show how smart you are,you could have slowed down just a bit for those that are not as knowledgeable as you are, for I was very eager to get this but you lost me at the square root of 12, could have explained that part little more indept ,after that I lost my will in frustration to anger to carry on,thanks for getting my hopes up to being more intelligent in mathematical equations only to feel less than .
I loved the thorough, step-by-step breakdown. As a math tutor, I’m definitely going to need it!
This is all about the so-called abc-formula, very easy when you cannot factor a quadratic equation. It also contains the so-called Discriminant (b^2 - 4ac), which informs you about the 'fractionability' of a quadratic equation (if the D = 0 you can always fraction the equation) and about the kind of the solution ( 2 real numbers, one 'double' solution or also imaginary numbers as solution(s) ).
Amazing how a 5 minute explanation can be stretched into a longer, more boring explanation than I heard in 60's high school.
The Quadratic Formula: To the tune of Row Row Row your Boat: x equals minus b, plus or minus the square root of b squared minus four a c, all over two a.
Great experience, thank you, it can help with heaps of students who do not understand in equations like this! Thank you once again. God bless your online class,