To rewrite the equation from standard form to vertex form, follow these steps:

1. Start with the standard form equation:

\(y = x^2 - 6x - 6\)

2. Complete the square by adding and subtracting the square of half the coefficient of the x-term (\(-6/2 = -3\)):

\(y = x^2 - 6x + (-3)^2 - (-3)^2 - 6\)

3. Group the perfect square trinomial and constants:

\(y = (x^2 - 6x + 9) - 9 - 6\)

4. Simplify the perfect square trinomial and constants:

\(y = (x - 3)^2 - 15\)

So, the equation in vertex form is:

\(y = (x - 3)^2 - 15\)