Marcus needs to rewrite f (x) = x2 + 6x + 4 in vertex form.

Set f (x) = y

-> y = x^2 + 6x + 4

Now, subtract 4 from both sides.

-> y - 4 = x^2 + 6x

Complete the square (take half of six and square it) and add this to both sides.

-> y - 4 + 9 = x^2 + 6x + 9

Now we can rewrite x^2 + 6x + 9 with a perfect square.

-> y + 5 = (x + 3) ^2

Subtract 5.

-> y = (x + 3) ^2 - 5

Done.