Answer
Please see the graph.
Work Step by Step
$f(x)=x^2-1$
Axis of symmetry:
$f(x)=(x-0)^2-1$
$x=0$ is the axis of symmetry
Vertex:
$f(x)=x^2-1$
$x=0$
$f(0)=0^2-1$
$f(0)=0-1$
$f(0)=-1$
The vertex is the orange dot, the axis of symmetry is the black vertical line, and the green line is the function.