Answer
The x-intercepts are (-3,0) and (3,0)
The y-intercept is (0,9)
The equation has symmetry only with respect to the y-axis.
Work Step by Step
To find the x-intercept(s), we set y to 0 and solve for x:
$x^2+0=9$
$x^2=9$
$\sqrt{x^2}=\sqrt9$
$x=\pm3$
To find the y-intercept(s), we set x to y and solve for y:
$0^2+y=9$
$y=9$
To test for symmetry with respect to the x-axis, we substitute y for -y and check if it equals the original equation:
$x^2+(-y)=9$
$x^2-y=9$ nope
To test for symmetry with respect to the y-axis, we substitute x for -x and check if it equals the original equation:
$(-x)^2+y=9$
$x^2+y=9\checkmark$
To test for symmetry with respect to the origin, we substitute x for -x, substitute y for -y and check if it equals the original equation:
$(-x)^2+(-y)=9$
$x^2-y=9$ nope