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