Answer:
[tex]g(x)=(x-8)^2-64[/tex]
Step-by-step explanation:
The given function is;
[tex]g(x)=-16x+x^2[/tex]
This is the same as;
[tex]g(x)=x^2-16x[/tex]
Add and subtract the square of half the coefficient of x.
[tex]g(x)=x^2-16x+(-8)^2-(-8)^2[/tex]
Observe that the first three terms is a perfect square trinomial.
[tex]g(x)=(x-8)^2-64[/tex]
The vertex form is [tex]g(x)=(x-8)^2-64[/tex]
The vertex (8,-64)
