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

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

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=(-b)/(2a)`

k - its value of y for x = h.

We have

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

`h=(-(-32))/(2(2))=(32)/(4)=8`

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