Answer
parabola, vertex $(1,-\frac{1}{2})$, focus $(1,\frac{3}{2})$, and directrix $y=-\frac{5}{2}$.
Work Step by Step
1. Given $8y=(x-1)^2-4$ or $(x-1)^2=8(y+\frac{1}{2})$, we can identify the equation as a parabola opens upward with $p=2$.
2. We can find its vertex $(1,-\frac{1}{2})$, focus $(1,\frac{3}{2})$, and directrix $y=-\frac{5}{2}$.
