When completing the square you room aiming to compose your function in the format:

a(x+b)^2 + c

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

4x^2 + 12x + 9 = 0

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

Looking simply inside the parentheses we room aiming to create this expression together a square. Starting with simply the x^2 and 3x terms we will shot to write them as a square the will an outcome in x^2 + 3x however not worry around the constant term that outcomes yet.

You are watching: 4x^2+12x+9

(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 specifically matches our initial expression, no further manipulation is necessary for the constant term meaning we can rewrite the original role as:

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


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