Answer
symmetric with respect to the $y$-axis.
Work Step by Step
Step 1. To test $x$-axis symmetry, replace $(x,y)$ with $(x,-y)$, we have $-y=5x^2-1$ which is equivalent to $y=-5x^2+1$. This is different from the original equation, thus it is not symmetric with respect to the $x$-axis.
Step 2. To test $y$-axis symmetry, replace $(x,y)$ with $(-x,y)$, we have $y=5(-x)^2-1$, which is equivalent to $y=5x^2-1$, the original equation. Thus, the function's grap is symmetric with respect to the $y$-axis.
Step 3. To test origin symmetry, replace $(x,y)$ with $(-x,-y)$, we have $-y=5(-x)^2-1$ which when simplified becomes $y=-5x^2+1$. This is different from the original equation, thus it is not symmetric with respect to the origin
