Answer
Please see the graph.
Axis of symmetry: $x=0$
Vertex: $(0, -4)$
Work Step by Step
$f(x)=x^2-4$
$a=1$, $b=0$, $c=-4$
$x=-b/2a$ is the vertex.
$x=-0/2*1$
$x=0/2$
$x=0$
$f(x)=x^2-4$
$f(0)=0^2-4$
$f(0)=0-4$
$f(0)=-4$
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