Answer
domain $[-4,\infty)$, range $(-\infty,\infty)$,
vertex $(-4,-1)$, axis of symmetry as $y=-1$.
See graph.
Work Step by Step
1. Rewrite the equation as $x=4(y^2+2y+1)-4=4(y+1)^2-4$ or $(y+1)^2=\frac{1}{4}(x+4)$
2. We can identify its domain as $[-4,\infty)$ and range as $(-\infty,\infty)$
3. We can find its vertex at $(-4,-1)$ and axis of symmetry as $y=-1$
4. See graph.
