## Precalculus: Concepts Through Functions, A Unit Circle Approach to Trigonometry (3rd Edition)

The equation's graph is symmetric only with respect to the $y$-axis.
We have $y=5x^2-1$. (1) To test for symmetry about $x$-axis we replace $y$ by $-y$. If the resulting equation is exactly the same as the original, then the function's graph is symmetric with respect to the $x$-axis. $-y=5x^2-1$ This equation is not the same as the original hence there is no symmetry about the $x$-axis. (2) To test the symmetry about y-axis we replace $x$ by $-x$. If the resulting equation is exactly the same as the original, then the function's graph is symmetric with respect to the $y$-axis. $y=5(-x)^2-1=5x^2-1$ This equation is the same as the original function hence there is symmetry about the $y$-axis. (3) To test the symmetry about the origin we replace $x$ by $-x$ and $y$ by $-y$. If the resulting equation is exactly the same as the original, then the function's graph is symmetric with respect to the origin. $-y=5(-x)^2-1\\ -y=5x^2-1.$ This equation is not the same as the original hence there is no symmetry about the origin.