Answer
$$ (1,-2)$$
Work Step by Step
Completing the square in order to write the equation in the form $a(x-h)^2+k$, we find:
$$-4\left(x^2-2x+\frac{3}{2}+\left(-1\right)^2-\left(-1\right)^2\right) \\ -4\left(\left(x-1\right)^2+\frac{3}{2}-\left(-1\right)^2\right) \\ -4\left(x-1\right)^2-2$$
The vertex is $(h,k)$, so we see that the vertex is:
$$ (1,-2)$$
