Answer
vertex $(2,-2)$, focus $(2,-\frac{3}{2})$, and directrix $y=-\frac{5}{2}$; see figure.
Work Step by Step
Step 1. Rewrite the equation as $x^2-4x+4=2y+4$ or $(x-2)^2=2(y+2)$; we have $p=\frac{2}{4}=\frac{1}{2}$
Step 2. We can identify that this parabola opens upwards with a vertex at $(2,-2)$, focus at $(2,-2+\frac{1}{2})$ or $(2,-\frac{3}{2})$, and directrix as $y=-2-\frac{1}{2}=-\frac{5}{2}$
Step 3. We can graph the equation as shown in the figure.
