Answer
$$ (-3,-6)$$
Work Step by Step
Completing the square in order to write the equation in the form $a(x-h)^2+k$, we find:
$$\left(x+3\right)^2+3-3^2\\ \left(x+3\right)^2-6$$
The vertex is $(h,k)$, so we see that the vertex is:
$$ (-3,-6)$$