Answer
There is only a symmetry about the x-axis.
See graph.
The intercepts: $(-1,0)$, $(0,-1)$, $(0,1)$.
Work Step by Step
$$x=y^2-1$$
Testing for the symmetry about the x-axis:
$$x=(-y)^2-1$$ $$x=y^2-1$$
Since the resulting equation is the same as the original equation, there is symmetry about the x-axis.
Testing for the symmetry about the y-axis:
$$-x=y^2-1$$ $$x=-y^2+1$$
Since the resulting equation is not the same as the original equation, there is no symmetry about the y-axis.
Testing for the symmetry about the origin:
$$-x=(-y)^2-1$$ $$-x=y^2-1$$ $$x=-y^2+1$$
Since the resulting equation is not the same as the original equation, there is no symmetry about the origin.
For $y=0$:
$$x=0^2-1=-1$$
For $y=1$:
$$x=1^2-1=0$$
For $y=-1$:
$$x=(-1)^2-1=0$$
Thus, three points on the curve are at $(-1,0)$, $(1,0)$ and $(-1,0)$.
Using the three points, the graph is as shown.
The intercepts are as for x-intercept is $(-1,0)$, and for y-intercepts are $(0,-1)$ and $(0,1)$.
