Answer
Please see the graph.
Work Step by Step
$g(x) = (x+2)^2-5$
Axis of symmetry:
$g(x) = (x+2)^2-5$
$g(x) = (x- -2)^2-5$
$x=-2$
Vertex:
$g(x) = (x+2)^2-5$
$g(-2) = (-2+2)^2-5$
$g(-2)=0^2-5$
$g(-2) = 0-5$
$g(-2)=-5$
The green line $x=-2$ is the axis of symmetry, the black dot at $(-2,-5)$ is the vertex, and the red line is the function $h(x)=(x+2)^2-5$.
