Question

The first three steps in writing f(x) = 40x + 5x2 in vertex form are shown.

Write the function in standard form. f(x) = 5x2 + 40x
Factor a out of the first two terms. f(x) = 5(x2 + 8x)
Form a perfect square trinomial. (eight-halves) squared = 16
f(x) = 5(x2 + 8x + 16) – 5(16)
What is the function written in vertex form?

f(x) = 5(x + 4) – 80
f(x) = 5(x + 8) – 80
f(x) = 5(x + 4)2 – 80
f(x) = 5(x + 8)2 – 80

Answer 1

f(x) = 5(x + 4)^2 − 80

Work: 5(x^2 + 8x) = 5(x^2 + 8x + 16 − 16) = 5[(x + 4)^2 − 16] = 5(x + 4)^2 − 80.