Answer
The given equation is symmetric with respect to the y-axis.
Work Step by Step
$\bf\text{Test for Symmetry with x-axis}$:
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.
