Answer:
f(x) = 3(x - 1)² - 12
Step-by-step explanation:
Given
f(x) = (3x - 9)(x + 1) ← expand factors using FOIL
= 3x² - 6x - 9
To complete the square the coefficient of the x² term must be 1
Factor 3 out of 3x² - 6x
f(x) = 3(x² - 2x) - 9
To complete the square
add/subtract ( half the coefficient of the x- term )² to x² - 2x
f(x) = 3(x² + 2(- 1)x + 1 - 1) - 9
= 3(x - 1)² - 3 - 9
= 3(x - 1)² - 12 ← equation in vertex form
