Answer
$$ (\frac{1}{2},\frac{15}{4})$$
Work Step by Step
Completing the square in order to write the equation in the form $a(x-h)^2+k$, we find:
$$\left(x-\frac{1}{2}\right)^2+4-\left(-\frac{1}{2}\right)^2 \\ \left(x-\frac{1}{2}\right)^2+\frac{15}{4}$$
The vertex is $(h,k)$, so we see that the vertex is:
$$ (\frac{1}{2},\frac{15}{4})$$