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