Answer
$$ (-\frac{3}{2},-\frac{21}{4})$$
Work Step by Step
Completing the square in order to write the equation in the form $a(x-h)^2+k$, we find:
$$x^2-3x-3+\left(-\frac{3}{2}\right)^2-\left(-\frac{3}{2}\right)^2 \\ \left(x-\frac{3}{2}\right)^2-3-\left(-\frac{3}{2}\right)^2 \\ \left(x-\frac{3}{2}\right)^2-\frac{21}{4}$$
The vertex is $(h,k)$, so we see that the vertex is:
$$ (-\frac{3}{2},-\frac{21}{4})$$
