Answer
parabola, vertex $(2,-2)$, focus $(2,-\frac{3}{2})$, and directrix $y=-\frac{5}{2}$.
Work Step by Step
1. Given $x^2-4x=2y$ or $(x-2)^2=2(y+2)$, we can identify it as a parabola opens upward with $p=\frac{1}{2}$.
2. We can find its vertex $(2,-2)$, focus $(2,-\frac{3}{2})$, and directrix $y=-\frac{5}{2}$.
