Question

What is the axis of symmetry and vertex for the graph `y= 1/2x^2`?

Answer 1

The vertex is `(0,0)` and the axis of symmetry is `x=0`.

Explanation:

The function `y=1/2x^2` is in the form `y=a*(x-h)^2+k` which has vertex `(h,k)`. The axis of symmetry is the vertical line through the vertex, so `x=h`.

Going back to the original `y=1/2x^2`, we can see by inspection that the vertex is `(0,0)`. The axis of symmetry, therefore, is `x=0`.