Answer
Symmetric to only x-axis
Work Step by Step
Substitute -x for x. If equation is equivalent, graph is symmetric to y-axis.
$y^{2}$=$(-x)^{3}$-8(-x)
$y^{2}$=$-x^{3}$+8x
Equations are not equivalent, so not symmetric to y-axis.
Substitute -y for y. If equation is equivalent, graph is symmetric to x-axis.
$(-y)^{2}$=$x^{3}$-8x
$y^{2}$=$x^{3}$-8x
Equivalent to initial equation, so symmetric with x-axis.
Substitute -y for y and -x for x. If equation is equivalent, graph is symmetric to origin.
$(-y)^{2}$=$(-x)^{3}$-8(-x)
$y^{2}$=$-x^{3}$+8x
Equations are not equivalent, so not symmetric to origin.
