Answer
vertex $(-4,-2)$, focus $(-4,-1)$, directrix $y=-3$
See graph.
Work Step by Step
1. We can identify that $x^2+8x=4y-8\Longrightarrow (x+4)^2=4(y+2)$ is a parabola opens upward,
2. Compare with the standard form to get:
$p=1$, vertex $(-4,-2)$, focus $(-4,-1)$, directrix $y=-3$
3. Use symmetry and a few test points such as at $x=-1,-2,-3,-4$ to get the graph.
