Parabola vertex and axis of symmetry | Quadratic equations | Algebra I | Khan Academy

Parabola vertex and axis of symmetry

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Algebra I on Khan Academy: Algebra is the language through which we describe patterns. Think of it as a shorthand, of sorts. As opposed to having to do something over and over again, algebra gives you a simple way to express that repetitive process. It's also seen as a "gatekeeper" subject. Once you achieve an understanding of algebra, the higher-level math subjects become accessible to you. Without it, it's impossible to move forward. It's used by people with lots of different jobs, like carpentry, engineering, and fashion design. In these tutorials, we'll cover a lot of ground. Some of the topics include linear equations, linear inequalities, linear functions, systems of equations, factoring expressions, quadratic expressions, exponents, functions, and ratios.

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[bethmoth]

I was lost then you explained the quicker way. Thanks

[michalvojacek]

Or, using calculus, which might be harder to do, but is more intuitive; you could set the equation's derivative equal to zero and solve for x. Because a derivative of a function is the rate of change of that function at a specific point, the vertex would be where the rate of change is zero, or, to put it geometrically, where its tangent is parallel to the x-axis:
(Using Lagrange's notation)
Useful: (x^n)' = nx^(n-1)

(-2x+8x+8)' = 0
-2*2*x+8 = 0
-4x+8 = 0
-4x = -8
4x = 8
x = 2

To get the Y of the vertex you just have to evaluate the original expression at the x we got:

-2x^2+8x+8
= -2*2^2 + 8*2 + 8
= -2*4 +16 +8
= -8 + 16 +8
= 16 + 8 -8
= 16

And there you go:
The vertex is at [2; 16]

(Btw. if you don't know what I just did don't worry, you'll learn some day)

[jenxberry]

I just learned more in a 7 minute video than in a whole week in my Math class. *gReAt*

[popeyes]

The quarantine packets don't teach squat so ty so much
Also if your hear for Axis of Symmetry or shortcut then it starts at 6:28

[WesternkindUnited]

slow and intuitive way no exact opposite of what I need. I need a simple formula to apply and get this miserable experience over with.

[helenpetersen]

Oh.My.God. BRUH that shortcut may have just saved my final tomorrow! Why didn't my teacher have the foresight to teach us that!!! I've been confused on the vertex for two weeks! 😧😧😧

[UGLYRAED]

YAY now I know both methods.
Quick and dirty is not allowed on youtube.hope this video doesn't get deleted

[Bella-dosh]

This is why I love Khan Academy. You always answer the question why?

[e.hamrick]

3:40 That is not always true. If you substitute 2 for "x", and then complete the operation inside of the parenthesis and then square it, then you won't have a positive number. You will get 0, which is neither positive nor negative. 3:52 Same thing, it won't always be negative. If you have a difference of 0 in the parenthesis like I explained earlier, then you will not have a negative number (since zero times anything is zero), but rather, zero, which is neither negative nor positive. Thank you for taking the time to read this.

[naomidemenezes]

Algebraically arranging the equation definitely helps out when looking for or defining your maximum or minimum point. Although, the quick and dirty way of finding the vertex is simple and a lot quicker than going through each step to find the vertex.

[Echo-wpul]

Good video, with a small error at the end : for x=3 y=6, not 8.

for y=8 value of x must be 4 - which is visible on the graph

[demshi]

thanks bro!!! i finally got it! after hours trying to figure it out how to graph q. f . ^____^ u made it easy for me . u r the best !1

[zaraf]

I now may not fail my maths test tomorrow so thanks

[jffrysith]

Thank you. Ive been trying to teach this formula but I didnt really know how to derive it because its not taught in NZ.
I figured it out half wah through the video because your explanations are amazing!!

[THETHPHANTOM]

I'll take the hooligan formula thank you.

[Roxannev]

Come on down to Olive Garden and get yo free breadsticks 🥖🥖

[sri-kaushalramana]

wait how do u get the y value from the shortcut, didn't say

[IanSerranoBengoa]

i came here for the axis of symmetry... where did you explain that? bro the mumble you made was so fast i almost didn't catch, and well... i didn't understand it either but i got everything else, you are a pretty good tutor, just dont put axis of symmetry in the title if you aint going to explain it, or even write it. still 10/10, love the colors!

[stephhmph]

THANK YOU FOR TEACHING ME. Unlikes my teacher has been able to.

[xue]

Lol when ur math teacher just goes “watch khan” 😂