Rewrite the function by completing the square. f(x)=4x^2+12x+9

Answer 1

When completing the square you are aiming to write your function in the format:

a(x+b)^2 + c

The first step will be factoring out the coefficient modifying the x^2 term; in this case 4:

4x^2 + 12x + 9 = 0

4(x^2 + 3x + 9/4) = 0

Looking just inside the parentheses we are aiming to write this expression as a square. Starting with just the x^2 and 3x terms we will try to write them as a square that will result in x^2 + 3x but not worry about the constant term that results yet.

(x + 3/2)^2

(x + 3/2)*(x + 3/2)

x^2 + 3x/2 + 3x/2 + 9/4

x^2+ 3x + 9/4

Because this exactly matches our original expression, no further manipulation is needed for the constant term meaning we can rewrite the original function as:

f(x) = 4(x + 3/2)^2