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

The vertex is $\left(0 , 0\right)$ and the axis of symmetry is $x = 0$.
The function $y = \frac{1}{2} {x}^{2}$ is in the form $y = a \cdot {\left(x - h\right)}^{2} + k$ which has vertex $\left(h , k\right)$. The axis of symmetry is the vertical line through the vertex, so $x = h$.
Going back to the original $y = \frac{1}{2} {x}^{2}$, we can see by inspection that the vertex is $\left(0 , 0\right)$. The axis of symmetry, therefore, is $x = 0$.