Answer
Symmetry with respect to the $y$-axis
Work Step by Step
Testing symmetry with respect to $x$-axis:
$$-y=-x^4+6x^2$$ $$y=x^4-6x^2$$
Since the resulting equation is not the same as the original equation, the equation is not symmetric with respect to $x$-axis.
Testing symmetry with respect to $y$-axis:
$$y=-(-x)^4+6(-x)^2$$ $$y=-x^4+6x^2$$
Since the resulting equation is the same as the original equation, the equation is symmetric with respect to $y$-axis.
Testing symmetry with respect to origin:
$$-y=-(-x)^4+6(-x)^2$$ $$-y=-x^4+6x^2$$ $$y=x^4-6x^2$$
Since the resulting equation is not the same as the original equation, the equation is not symmetric with respect to origin.
The sketch of the graph is as shown.
