Question

How do convert this equation from standard form to vertex form? y=3x^2-96x+1024

Answer 1

factorize, then by using completing square
y=3x^2-96x+1024
y=3(x^2-32x+256) + 256
y=3(x^2-16x)^2 + 256

Answer 2

opppsss.. i meant
y=3(x^2-16)^2 + 256

Answer 3

Or you can just find the vertex first. Then insert it into the vertex formula \(y = a(x - h)^2 + k\) You already have the value of a = 3

Answer 4

The vertex will be the point \((h,k)\)

Answer 5

@GAzela1997, do you know how to find the vertex of a parabola?

Answer 6

yep got it so you add them together and divide it by 2

Answer 7

I think

Answer 8

@tHe_FiZiCx99 are you still typing?

Answer 9

\(\ \boxed{\boxed{\boxed{\color{red}{\huge\heartsuit\boxed{H}}\color{green}{\boxed{E}}\color{green}{\small\boxed{L}}\color{green}{\boxed{L}}\color{blue}{\huge\boxed{O}}\color{blue}{\huge\heartsuit}}}} \)

↑ Lol, I had to xD


The vertex of a parabola is found using: \(\ \sf \dfrac{-b}{2a} \)

y = 3x^2 -96x + 1024

Subtract 1024 from both sides, \(\ -1024 = 3x^2 - 96x + \dfrac{\cancel{1024}}{\cancel{-1024}} \) <-- Latex ;-; . . they basically cancel out.


-1024 = 3x^2 - 96x . . .Factor out the "3" from 3x^2 - 96.

-1024 = 3(x^2 - 32\(\ \sf\color{blue}{x}\)) now take half of the "\(\ \sf \color{blue}{x}\)" term.

\(\ \dfrac{-32}{2} = -16 \) now sqaure it. -16^2 = 256

-1024 = 3(x^2 - 32x + 256), take 56 and subtract it from the equation but keep it there. I'm horrible at explaining things, bear with me.

-1024 = 3(x^2 - 32x + 256 [- 256]) . . . Before you add 1024 to both sides, you multiply -256 by 3.

y = 3(x^2 - 32x + 256) - 768. Now you can add 1024 to both sides.

y = 3(x^2 - 32x + 256) + 256

A shortcut is to take (x^2 - 32x + 256) and square-root it. It'll always be half the "x" term keeping the sign. (x - 16)^2

y = 3(x - 16)^2 + 256

And that's vertex form. Where: \(\ \sf y = \color{red}{a}(x - \color{blue}{h})^2 + \color{green}{k} \)

\(\ \sf y = \color{red}{3}(x - \color{blue}{16})^2 + \color{green}{256} \)

The vertex is \(\ (\color{blue}{h},\color{green}{k})\), so, \(\ (\color{blue}{16},\color{green}{256}\))

You can also find the axis of symmetry with the vertex, it's the x coordinate in the vertex coordinate. So yours is (16), where the parabola can be cut in half.

Answer 10

@Hero Yes. My internet keeps lagging. . .

Answer 11

;_; I made a typo