Answer
$$ (-\frac{1}{6},-\frac{23}{12})$$
Work Step by Step
Completing the square in order to write the equation in the form $a(x-h)^2+k$, we find:
$$-3\left(\left(x+\frac{1}{6}\right)^2+\frac{2}{3}-\left(\frac{1}{6}\right)^2\right) \\ -3\left(x+\frac{1}{6}\right)^2-\frac{23}{12}$$
The vertex is $(h,k)$, so we see that the vertex is:
$$ (-\frac{1}{6},-\frac{23}{12})$$
