Answer
vertex $(2,-2)$, focus $(2, -\frac{3}{2})$, directrix $y=-\frac{5}{2}$
See graph.
Work Step by Step
1. We can identify that $x^2-4x=2y\Longrightarrow (x-2)^2=2(y+2)$ is a parabola opens upward,
2. Compare with the standard form to get:
$p=\frac{1}{2}$, vertex $(2,-2)$, focus $(2, -\frac{3}{2})$, directrix $y=-\frac{5}{2}$
3. Use symmetry and a few test points such as at $x=0,1,2$ to get the graph.
