## Precalculus (6th Edition) Blitzer

The graph of an equation is symmetric with respect to the y-axis if substituting $-x\text{ for }x$ in the equation results in an equivalent equation.
We know that if the graph of a function is symmetric about y-axis, then it is an even function and if replacement of $x$ by $-x$, there will be no effect on the function. For example, $y={{x}^{2}}+2$ Replace $x$ by $-x$: \begin{align} & y={{\left( -x \right)}^{2}}+2 \\ & y={{x}^{2}}+2 \\ \end{align} Thus, this equation is an equivalent equation. So, the graph will be symmetric with respect to the y-axis.