Answer
$$ (\frac{7}{4},-\frac{25}{8})$$
Work Step by Step
Completing the square in order to write the equation in the form $a(x-h)^2+k$, we find:
$$2\left(x^2-\frac{7x}{2}+\frac{3}{2}+\left(-\frac{7}{4}\right)^2-\left(-\frac{7}{4}\right)^2\right) \\ 2\left(\left(x-\frac{7}{4}\right)^2+\frac{3}{2}-\left(-\frac{7}{4}\right)^2\right) \\ 2\left(x-\frac{7}{4}\right)^2-\frac{25}{8}$$
The vertex is $(h,k)$, so we see that the vertex is:
$$ (\frac{7}{4},-\frac{25}{8})$$
