Question

The first steps in writing f(x) = 4x2 + 48x + 10 in vertex form are shown. f(x) = 4(x2 + 12x) + 10 = 36 What is the function written in vertex form?

Answer 1

f(x) = 4x² + 48x + 10 = 36

Take out the coefficient of x²:

4(x² + 12x) + 10 = 36

Take away 10 from both sides:

4(x² + 12x)  = 26

Divide both sides by 4:

x² + 12x  = 6.5

Add in (b/2)² on both sides:

x² + 12x + (12/2)²  = 6.5 + (12/2)²

x² + 12x + 6²  = 42.5

Form perfect square:

(x + 6)² = 42.5

Subtract 42.5 from both sides:

(x + 6)² - 42.5 = 0

Answer: f(x) = (x + 6)² - 42.5