vertex form is y=a(x-h)²+k
complete the square
f(x)=(-x²+8x)+9
undistribute -1
f(x)=-1(x²-8x)+9
take 1/2 of -8 and square it to get 16, then add neagative and positive inside
f(x)=-1(x²-8x+16-16)+9
complete the square
f(x)=-1((x-4)²-16)+9
expand
f(x)=-1(x-4)²+16+9
f(x)=-1(x-4)²+25
vertex form is
f(x)=-1(x-4)²+25