Answer
Vertex: $(0,c)$
Axis of symmetry: $x=0$
Work Step by Step
The vertex of the the quadratic function $y=ax^2+c$ is the vertex of the parent function $y=x^2$ vertically translated by $c$ units:
$$(0,c)$$
The axis of symmetry is the same as that of the parent function:
$$x=0$$