Answer
Please see the graph.
Work Step by Step
$h(x) = (x+4)^2-6$
Axis of symmetry:
$h(x) = (x+4)^2-6$
$h(x) = (x- -4)^2-6$
$x=-4$
Vertex:
$h(x) = (x+4)^2-6$
$h(-4) = (-4+4)^2-6$
$h(-4)=0^2-6$
$h(-4) = 0-6$
$h(-4)=-6$
The green line $x=-4$ is the axis of symmetry, the black dot at $(-4,-6)$ is the vertex, and the red line is the function $h(x)=(x+4)^2-6$.
