Which function in vertex form is equivalent to f(x) = x2 + 8 – 16x?

F(x) = y = x² -16x + 8 is a parabola and it's standard form is:

(y-k) = a(x-h)², since a =1, our standard form will be (y-k) = (x-h)².

to get the standard form we have to complete the square of (x² -16) +8
completing the square of (x-16x²), gives (x-8)² - 64:
so y = [(x-8)² -64] + 8 
  y = (x-8)² - 56 ; transpose - 56 to the left;
y+56 =  (x-8)² this is the answer