Question

Consider the function ƒ(x) = 3x2 + 6x + 5.

Write the function in the form of ƒ(x) = a(x – h)2 + k, where a, h and k are constants.

Answer 1

f(x) = 3(x + 1)² + 2

Explanation:

Use the method of completing the square

3x² + 6x + 5

= 3(x² + 2x) + 5

add/ subtract (half the coefficient of the x-term)² to x² + 2x

= 3(x² + 2(1)x + 1 - 1) + 5

= 3(x + 1)² - 3 + 5

f(x) = 3(x + 1)² + 2 ← in vertex form