Answer :
Answer:
[tex]\large\boxed{y=2(x-8)^2-72}\\\boxed{minimum\ is\ -72\ for\ x=8}[/tex]
Step-by-step explanation:
[tex]y=a(x-h)^2+k[/tex]
It's the vertex form of a quadratic equation of [tex]y=ax^2+bx+c[/tex]
The vertex is at (h, k).
k is minimum or maximum for value of h.
[tex]h=\dfrac{-b}{2a}[/tex]
k - its value of y for x = h.
We have
[tex]y=2x^2-32x+56\\\\a=2,\ b=-32,\ c=56[/tex]
[tex]h=\dfrac{-(-32)}{2(2)}=\dfrac{32}{4}=8[/tex]
[tex]k=2(8^2)-32(8)+56=2(64)-256+56=128-256+56=-72[/tex