Answer
Please see the graph.
Work Step by Step
$h(x) = -3(x+3)^2+1$
Axis of symmetry:
$h(x) = -3(x+3)^2+1$
$h(x) = -3(x- -3)^2+1$
$x=-3$
Vertex:
$h(x) = -3(x+3)^2+1$
$h(-3) = -3(-3+3)^2+1$
$h(-3) = -3(0)^2+1$
$h(-3) = 0+1$
$h(-3) = 1$
The red line is the function $h(x)=-3(x+3)^2+1$, the green line at $x=-3$ is the axis of symmetry, and the point $(-3,1)$ is the vertex.
