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