Which function in vertex form is equivalent to f(x) = x² + 8 - 16x?
A.f(x) = (x - 8)² – 56
B.f(x) = (x - 4)² + 0
C.f(x) = (x + 8)² - 72
D.f(x) = (x + 4)² - 32

Solution:

The given function is

f(x) = x² + 8 - 16x

We can write it as

y = x² - 16x + 8

y - 8 = x² - 16x

By adding 64 on both sides

y - 8 + 64 = x² - 16x + 64

y + 56 = (x - 8)²

So we get

y = (x - 8)² - 56

Therefore, the function in vertex form is f(x) = (x - 8)² - 56.

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

Summary:

The function f(x) = (x - 8)² - 56 in vertex form is equivalent to f(x) = x² + 8 - 16x.