Question

what is y=2x^2-32x+56 rewritten in the form of y=a(x-h)^2+k ? and what is the x-coordianate of the mininum?​

Answer 1

Answer:

$\large\boxed{y=2(x-8)^2-72}\\\boxed{minimum\ is\ -72\ for\ x=8}$

Step-by-step explanation:

$y=a(x-h)^2+k$

It's the vertex form of a quadratic equation of $y=ax^2+bx+c$

The vertex is at (h, k).

k is minimum or maximum for value of h.

$h=\dfrac{-b}{2a}$

k - its value of y for x = h.

We have

$y=2x^2-32x+56\\\\a=2,\ b=-32,\ c=56$

$h=\dfrac{-(-32)}{2(2)}=\dfrac{32}{4}=8$

[tex]k=2(8^2)-32(8)+56=2(64)-256+56=128-256+56=-72[/tex