## Precalculus (6th Edition) Blitzer

The equation in the example is symmetric with respect to the $y$-axis.
To verify that the equation is symmetric with respect of the $y$ -axis, substitute $x=-x$ in the above equation. If after putting $x=-x$, the resultant equation is the same as the given equation, then the equation is symmetric with respect to the $y$-axis. \begin{align} & y={{x}^{2}}-2 \\ & y={{\left( -x \right)}^{2}}-2\text{ } \\ & y={{x}^{2}}-2 \end{align} Since the resultant equation is the same as the given equation, the equation is symmetric with respect to the $y$-axis.