Answer
Please see the graph.
Work Step by Step
$h(x) = (x+1)^2+4$
Axis of symmetry:
$h(x) = (x+1)^2+4$
$h(x) = (x- -1)^2+4$
$x=-1$
Vertex:
$h(x) = (x+1)^2+4$
$h(-1) = (-1+1)^2+4$
$h(-1)=0^2+4$
$h(-1) = 0+4$
$h(-1)=4$
The green line $x=-1$ is the axis of symmetry, the black dot at $(-1,4)$ is the vertex, and the red line is the function $h(x)=(x+1)^2+4$.
