Question

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

f(x) = (x – 8)2 – 56
f(x) = (x – 4)2 + 0
f(x) = (x + 8)2 – 72
f(x) = (x + 4)2 – 32

Answer 1

Start with f(x) = x^2 - 16x + 8. Complete the square:

x^2 - 16x + 8 = (x^2 - 16x + 64) + 8 - 64 = (x - 8)^2 - 56.

So the equivalent vertex-form is f(x) = (x – 8)^2 – 56.