Graphing Higher-Degree Polynomials: The Leading Coefficient Test and Finding Zeros
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- Опубліковано 20 лис 2017
- By now, graphing lines seems trivial, and even graphing quadratics is a piece of cake. But what about higher-degree polynomials like cubics, quartics, and quintics? And even higher than that? It might seem quite daunting, but there are some handy tricks that will help you graph even these very complex functions. These involve using the leading coefficient test to discern the end behavior of the function, as well as plotting zeros and assessing their multiplicities in order to get a rough sketch of the function. It's not as bad as it sounds, check it out!
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I have a test tomorrow, thank you so much...
@Latifa Alawadhi this comment was made 9 months ago man, the guy passed the course already lmfao
mine is in an hour 😳
@@ciaraboone mine in 3 hours
Nah I ALREADY did the test.
Teacher wants me to show work so I put this LMFAO
@@ciaraboone soo sad...🤣
Thank you for explaining everything better than my teacher lmao
Yeah those hearts are only restricted to beauties.
tthank you so much for making this video I really had no idea where to start with these problems
thanks professor for making this video.it has further motivated me in loving the algebra
This is by far the best channel for explanations. I love how clear and visual you are, plus you answer the "whys" of math (to get the max we need calculus). Thank you
thank you so much! I am currently studying for a math cst test and this helped clear up some difficulties I had with higher order polynomials! thank you
Hii
Hi, nice video. I recommend you also to explain how to plot polynomials of multiple variables. It would be great)
Hi there, would you like to make a series about Elliptic Curve Cryptography (ECC) in future? I would love to learn from you.
There is a small error in the video: when he says that you can also use the y-intercept, he puts the y-intercept of the function somewhere around -2/3, but if you actually calculate the y-intercept by replacing all x'es with a 0, you can see that the y-intercept is (0, -3), so the drawing is incorrect, the extrema of the function are way more outspoken.
Yep
Yeah
He’s not wrong the x and y axis don’t have to follow the same scale.
Yup...
Will you have cheat sheet pdfs that cover everything that can be used to be printed out or saved? Or do i just have to take notes on the video?
I’ve thought about doing PDFs but it’s a lot of work, I suggest just taking full screen screenshots to make your own little slides.
The equation in the comprehension question should be x^4 + 5x^2 + 4 = y because x^4 + 5x^2 + 4 = 0 does not contain y, and is only used to find the x-intercepts; it is not the equation that we actually want to graph, which must contain y for the given answer.
Right sir
it is a hidden quadratic
This guy is a big help ❤️
Holy shit you explained this so perfectly my math teacher could never
Thank you very much, This is so helpful.
thank you this is exactly what i needed
Thank you very much professor
Hi, what's the solution of the factoring?
thanks.
Thank you!
Finally......., I got it ....., Thanks a lot sir😍😍
i understood everything except for the factorization of the comprehension exercise, can someone explain it to me? plz?
Very infotmative. Impressive. I'll be subscribing
this tutorial is Damn good I think im' get at least check in this part of the quiz tomorrow
shut up
@@foodisgood7607 Shut up
6:49 UA-cam’s red line is jumping out
Thank you, sir.
I have a test later. Thank you!
Thanks for clearing my concepts of this topic
Very nice method of teaching
Can someone explain me the comprehension quiz
professor, can you help me please the how to compute the apparent weight of a 60kg student standing inside a lift while he accelerates 2m /s square down ward, at rest and 2m /s square up ward, Just its formula pease.
thank you, god of math
Great explanations
But 😄😄 how did you study on your own to understand at such deeper level?!!😁😁😁(aka your study tricks)
i see 2 zero does it get multiplied and gives 4?
thank u for that saved my time
has to be y=4 specifically on x=0 on the comprehesion test or nah?
and how do i get 4 do i just plug in 0 on the x
like on the (x+1)(x-1)(x+2)(x-2) because if you plug 0 in you do get +4
YOU ARE THE BEST -from KICS
Thankyou!
Superb.
Thankyou so muchhhh
If all math teachers were like him or has his attitude I think many students wont need to watch this type of videos.
Thanks sir
I can't find the zeroes in the given question using the synthetic division. Can someone pls give a method to find the zeroes
rational roots test, it's covered in my tutorial on synthetic division
You can also use the quadratic formula just rearrange it like this and you would be able to find x^2.
(x^2)^2 - 5(x^2) + 4 = 0
Thank you
How did you factor? I don't understand how you got the (x+3)(x+1)(x-1) at 3:43
I know how to factor but this is confusing me a little. 😩
Trinity Lugo x^3+3x^2-x-3
Split in two pieces x^3+ 3x and -x-3
Factor each x^2( x+3) and -1(x+3)
Now combine (x^2-1)(x+3)
Factor x^2-1
X+1 x-1
Now you have x+3 x-1 x+1
@@eneu9069 alright, i can understand that a bit. Hopefully I can apply that to what I'm doing. 😓
Thank you so much for the clarification.
Trinity Lugo yea np we’re all here for help
The method is factoring bu grouping.
@@eneu9069 8:30 in this one a same procedure of it? kinda confuse
you just explained everything my math teacher failed to do in a semester lol. thanks
you can get the y values by plugging the x'es in the equation.
this is way better than going to school💕
I literally understand it😎
thanks again 😄
can someone explain to me how he resolved the comprehension equation?
nvm I got it
Thank you, Math Jesus
Ofc Professor Dave has a video on every topic I need to study. (insert a blessing from the lord meme here)
I still don't get it. How would you know how high will the turning point be till it goes back down or up?
we're dont. thats bc it's just sketch
it's just a rough idea about the graph of polynomial
thank you, I have an algebra II test tomorrow and you probably saved me a failing grade.
3:46 How did we get (x+3)(x+1)(x-1)=0?
factors of 3x2
3 times 1 times -1 is 3, and -3
Uh when i tried to make the zeros in the checking comprehension its (x + 1)(x + 4i)
its a negative 5 bro
Can you explain maxima and minima by using calculus
yes i have a tutorial on that! somewhere in the calculus section, has to do with second derivatives
watching while taking the test
Done.
I'm literally answering my module and I visit the link reference on our topic. Thank you so much for explaining. I had learned a lot. I can share this to my very late teacher who doesn't spend time discussing that is why I don't know anything without this video. HAHAAHAAHA
I have a test later and im gonna clutch it
I don't mean to be pedantic here, but if you graph the equation shown at 8:18, x^4 - 5x^2 + 4 = 0, you're going to end up with four vertical lines with x-intercepts at x={-2,-1,1,2}. It seems like what you are really asking your students to do is sketch the graph of f(x) = x^4 - 5x^2 +4.
Ty ^v^ again
for explains to me
I got my mistake made a mistake to consider the zeros to be even multiplicty thanks for the video
i didnt knew you explain math problems
thank you math jesus
"If you're confused, watch this clip one more time"
0:00
"If you're confused, watch this clip one more time"
0:00
"If you're confused, watch this clip one more time"
0:00
"If you're confused, watch this clip one more time"
0:00
"If you're confused, watch this clip one more time"
"What is up guuuuuys? I decided to become a UA-cam 'content' creator!" 😂😭
Nice intro
Lmao I'm watching to learn for the test and the example is the same on the test
I was looking for an explanation but I got the answer lolololol
Me writing this comment to come back and tell myself the grade I got
How much u got?
yeah how much did this guy get
@@xama5x. Oh yeah i forgot about this lol, got a solid 85% and ended my class with an A: 89.53 grade average!
@@Asian_Boii congratulations
thanks math jesus
It doesn't make any sense to me. 😵. Even though, thank you for teaching.
Is it cheating if I use a graphing calculator?
Depends on who's asking you to produce a graph of the equation.
thank you polynomial jesus
oh no 4:54
I wish you were my professor lol
ياريت تتاكدوا من جواز حكم وضع الموسيقى او الاغاني ع مقاطعكم عشان تتجنبوا الوقوع بالاثم وشكرا لكم ربي يحفظكم
Long hair
Beard
Helping people
Jesus is that you?
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I'm so dumb, i still don't get it...
Thanks Jesus
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Math Jesus
what the fuck im failing tomorrow
I can't understand a single thing
God loves you and he wants to save everyone, but in order for him to do that, you need to repent and be baptized. Also share his gospel with everyone you come in to contact with and keep his commandments 🙏🏾😘
This is a math tutorial, sweetie.
@@ProfessorDaveExplains Math loves you and wants to save everyone, but in order for math to do that, you need to revise and be educated. Also share this knowledge with everyone you come in to contact with and keep science alive 🙏🏾😘
There, fixed it for you 👍
men should only wear short hair
People don't "wear" hair, bud.
@@ProfessorDaveExplains 👏👏