Answer
$(y-4)^2=4(x+4)$
Parabola: vertex $V(-4, 4)$, focus $F(-3,4)$, directrix $x=-5$
See graph.
Work Step by Step
Step 1. Make squares of the variable: $y^2-8y=4x$, $(y-4)^2=4x+16$, or $(y-4)^2=4(x+4)$
Step 2. We can identify the conic as a parabola with a vertex at $V(-4, 4)$
Step 3. From the equation in step-1, we have $4p=4$ and $p=1$
Step 4. Use shifts from the center, we can identify the focus at $F(-3,4)$, and the directrix as $x=-5$
Step 5. Graph the function as shown.
