## College Algebra (10th Edition)

$\bf\text{Test for Symmetry with x-axis}$: Replace $y$ with $-y$ to obtain: $y=5x^2-1 \\-y=5x^2-1 \\-1(-y)=-1(5x^2-1) \\y=-5x^2+1$ The resulting equation is different from the original equation. Thus, the given equation is not symmetric with respect to the x-axis. $\bf\text{Test for Symmetry with y-axis}$: Replace $x$ with $-x$ to obtain: $y=5x^2-1 \\y=5(-x)^2-1 \\y=5x^2-1$ The resulting equation is the same as the original equation. Thus, the given equation is symmetric with respect to the y-axis. $\bf\text{Test for Symmetry with the Origin}$: Replace $x$ with $-x$ and $y$ with $-y$ to obtain: $y=5x^2-1 \\-y=5(-x)^2-1 \\-y=5x^2-1 \\-1(-y)=-1(5x^2-1) \\y=-5x^2+1$ The resulting equation is different from the original equation. Thus, the given equation is not symmetric with respect to the origin.