Given f (x) = x2+8x+13 . Enter the quadratic function in vertex form in the box. f (x) =

The vertex form of this equation is f (x) = (x + 4) ^2 - 3

In order to change an equation from standard form to vertex form, you must use a process called completing the square. To use this follow the steps below.

f (x) = x^2 + 8x + 13

Start by subtracting the constant from both sides.

f (x) - 13 = x^2 + 8x

Now take half of the coefficient of the x term and square it. Since the x term has a coefficient of 8, we take half of it (4) and square it (16). Now we add that to both sides.

f (x) - 13 + 16 = x^2 + 8x + 16

f (x) + 3 = x^2 + 8x + 16

Now that you've done these two steps, you can factor the right side into a perfect square.

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

And then we subtract the new constant from both sides.

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