Graphing Quadratic Functions (Precalculus - College Algebra 24)
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- Опубліковано 9 лют 2025
- Support: / professorleonard
Cool Mathy Merch: professor-leon...
A thorough explanation of graphing quadratics with reference to Vertex form by completing the square, the vertex formula, y intercepts, and x intercepts with the quadratic formula.
Completely unrelated to this Lecture. I just found out I passed calc 2 which was the bane of my existence. I would like to give 90% of the credit to Professor Leonard. He explains everything better than the entire textbook. Not only that he has a sense of humor and cares about his students. I want to thank you for everything you have done Professor Leonard!
Textbooks often have this obsession of being extremely formal and extremely serious all the time, and that alone makes them hard to follow - especially if they also ramble on forever for like 10 pages before giving a single example problem.
Professor Leonard is the complete opposite of that - he is much more like "alright, let's have some fun here, and let's cover the stuff that actually matters and then dive into a bunch of example problems".
Brilliant professor loved the way he teachs. Hats off. The superman of Maths.
I know I'm kinda off topic but do anyone know a good website to watch newly released movies online?
@Watson Zaire Try flixzone. You can find it on google :)
@Watson Zaire I watch on Flixzone. You can find it by googling =)
Professor Leonardo: * teaching math *
1st half of my brain: * trying to concentrate on what he's saying *
other half of brain: 'how do you get your arms to be that wide'
u da best at teaching math :D
I've had arms half that size at 13 but regardless, nice arms. ( Keep quiet )
Lots of silicon injections
@@johnbiluke8406 That's not that impressive lol ( im quiet)
@@fredavastine2922 dam ur stupid, try to go to the gym for a year or so, youll see major improvement, you wont get those arms jerking off, lmao
@@fredavastine2922 lolll, you clearly have never been to the gym
Professor Leonard thank you for a monster explanation of Graphing Quadratic Functions using the vertex, x intercepts, y intercepts, factoring and the old Quadratic Formula.
Best teacher in the whole world. A true SUPERMAN
Professor Leonard had his gym sessions and suddenly he realized he has to take Maths class. He comes to class and nails the lecture like a walk in the park...🙏🙏🙏
You are the best math teacher one can ever have. Thank you prof...Thank you for everything. 🙏
Hands down the best math teacher on internet.
Professor you’re a lifesaver thank you 🙏🏻
I am watching lots of maths tutorials during lockdown. Thanks for this video.
I’m sick right now but I love watching him teach math
Anxiously waiting for Linear Algebra and beyond.
really great video, it helped me a lot. thank you so much professor Leonard
Dude your jacked and your smart. Thank you so much!
He’s smarter AND hotter than my current math teacher! Very useful!
Thankx Professor these videos are helping me a lot
I am all over this :). Can't wait for the trig one's!
Thank you very much professor leonard .. the explanation is very easy to understand greetings from indonesia university
Thank you professor leonard I am in class 9 and it
Helped me a lot
Professor Leonard 🐐 GOAT
the best teacher ever
Thank you, Professor Leonard!
Thank you sir
Thanks for helping me to find my Vertex
Great profesor ever ♥️
Thank u so much leo
Sir You are The best ♥️
You are amazing. Can you do a video on synthetic division? :-(
I love the way you teach.
It makes sense.
Before, all of this intimidated me and made me feel stupid.
Thank you for everything.
I bought a shirt from your shop!
-V
engaging teacher,
I have a question Pr about limits:
lim [(theta^2) / (1 - cos (theta))] as theta approaches 0 = 2 (if we solve it by multiplying the expression by (1 + cos (theta))/(1 + cos (theta))).
However, when reviewing my notes, I tried to solve the above by this:
1. split factors
lim [(theta^2)/(1 - cos (theta))] as x -> 0 = lim [ theta * (theta/(1 - cos (theta)))] as x -> 0
2. Express the lim of my new product as a product of limits
lim [theta * (theta/(1 - cos (theta)))] as x -> 0 = lim theta as x -> 0 * lim theta/(1 - cos (theta)) as x -> 0
3. Use the fact that theta/(1 - cos (theta)) = ((1 - cos (theta))/theta)^-1
lim theta as x -> 0 * lim (theta/(1 - cos(theta))) as x -> 0 = theta * 0
-> lim [(theta^2) / (1 - cos(theta))] as x -> 0 = 0
The steps seem sound, but I don't get the same result as if I'd multiplied by the chosen 1, and I can't understand why.
Quadratic functions are amazing lol
Why is this recommended to me?!
I haven’t mathed in years...
Time to get back into it. It's the language of the universe.
You are in good luck, you have found the best channel in the world.
will you ever be doing a linear algebra series?
Prof, can we countercheck with desmos too? or, without calculating , can we use desmos right away?
Any idea when trigonometry section is gonna start?
it already started
when is the linear algebra segment coming up??
It almost a month, and you haven’t upload new videos of Precalculus. 🤧😭
Series is now completed!!
Great Leonardo
Hi professor i was wondering if there was any youtuber you would recomend for physics lessons?
I was just doing Quadratic programming for SVM and see this!
well this is my guy now! is this high school math?
Thank you.
I think I came up with a shortcut for finding 'a' when figuring out a formula. Take the two points you are given, (in the case of the video Vertex:(1, -5) and Y-int:(0, -3))
and minus the y value of the Vertex (-5) from the y value of the Y-int (-3) [-3-(-5)=2]. This will be the numerator of your fraction and the denominator will be the x value of the vertex squared [1^2=1] [a=2/1].
I'll give an example, let's say the Vertex is (-18, 7) and the Y-int is (0, -27).
-27-7=-34 (numerator).
-18^2=324 (denominator).
We get -34/324.
Now to verify -27=a(0+18)^2+7
-34=a*324
-34/324=a
I guess it ain't that much of a shortcut lol, but it feels faster when doing it in your head.
Thanks Sir
Thanks alot 😊
5:55 correct one is not 2a it must be 4a square
Vertex form at 50:00 should be f(x)=a(x-h)^2 + k not f(x)=a(x+h)^2 +k
can you teach us the solutions for all polynomials, such as ax4+bx3+cx2+dx+e=0 and many others with higher roots?
thank you.
Hi professor ! I did not understand at 33.39 time where did the 2 in front of the equation disappeared ?You did not use it when finding the Discriminant .Thanks
Hi Doc min 21.58 I do not understand how you plot the (1,2) and (-1,2 ) at 3rd quadrant .Thanks
Please, could someone explain to me how proffesor got 0 in 40:50 as y in vertex?
vertex is. point(-b/2a,f(-b/2a)) , here x coordinate (-b/2a) is -1/2 .
For y just solve for f(-1/2) which evaluates to 0.
vertex(x,y) = (-1/2,0)
Proff. Could u clear my doubt. I was just wondering that what is the condition for area to be negative under a polar curve if their is? Is it only possible when dtheta is negative?
to clarify doubts how can i get in touch with you sir.
Hi professor I need solutions to some questions in book mathematical arfekn, impossible?
6:00
What set do you rep?
and after you learn calculus and you realise where the first derivative equals zero, there is your x coordinate...
My man looks like clark kent i cant
23:00
Very nice lesson techquie. More graphical interface, I most like. Best regards.
Excuse me there professor I was wondering why many mathematicians never get into PDE’s don’t they take this class? They usually teach upto ODEs and stop there.
16:33 HAHAHAHAHA
He looks like the actor in superman🤔🤔
💯
SIR FROM WHICH BOOK YOU ARE TEACHING CALCULAS AND MULTIVARIABLE CALCULAS.
He has said he doesn't recommend a certain book. He has said to use multiple books. I recommend Early Transcendentals by Stewart if you have to pick one.
@@F4M05D4V35 thanks
more
Good afternoon sir.. do u lecture at the masters degree level?
Him:- calls this advanced algebra
Me:- we do this in grade 10 here in Nepal and it’s one of the most easiest problem
bruh Americans really make a big deal out of small things lmao
@@nuzhatazim8194 truu
I'm nepali but live in the US. Learning this stuff in 6th grade.
US curriculum is trash tho.
I'm in Canada. We do this in 5th grade.
I'm going to stop supporting this channel as a patreon until he uploads trigonometry videos just like the title of this Playlist says.
Your voice is echoing. You should probably use a collar microphone.
Sahil Dhingla bro this is free