how do u use the algebraic test 2 check for symmetry w/ both axes and the origin?

Question

x^2-y=0 ????
HELP!!!!!

Answer 1

Let (x, y) be an arbitrary point on the curve (satisfy the equation (x)^2 - (y) = 0).
If the curve is symmetric with x-axis, (x, -y) must also on the curve (satisfy the equation).
If the curve is symmetric with y-axis, (-x, y) must also on the curve (satisfy the equation).
If the curve is symmetric about the origin, (-x, -y) must also on the curve.
Now, (x)^2 - (-y) = x^2 +y = 0 is a different equation, the curve can not be symmetric with x-axis.
(-x)^2 - (y) = x^2 -y = 0 is the same equation, the curve must be symmetric with y-axis.
(-x)^2 - (-y) = x^2 +y = 0 is a different equation, the curve can not be symmetric about the origin.