Question

Rewrite the function by completing the square f(x) =4x2+12x+9

Answer 1

Answer:

see explanation

Step-by-step explanation:

Given

f(x) = 4x² + 12x + 9

The coefficient of the x² term must be 1 so factor out 4 from the first 2 terms

f(x) = 4(x² + 3x) + 9

To complete the square

add/ subtract ( half the coefficient of the x- term)² to x² + 3x

f(x) = 4(x² + 2($\frac{3}{2}$)x + $\frac{9}{4}$ - $\frac{9}{4}$) + 9

     = 4(x + $\frac{3}{2}$)² - 9 + 9

     = 4(x + $\frac{3}{2}$)²

Thus

f(x) = 4x² + 12x + 9 = 4(x + $\frac{3}{2}$)²