To check for symmetry on the x axis, replace y with –y
-y^2 –x(-y) =2
Apply the product rule, since the equation is not identical tot eh original equation it is not symmetric about the x axis
Now do the same for y axis by replacing x with –x
Again using product rule the equations are not identical, so it is not symmetric about the y axis
To check the origin,
Replace both x & y with –x & -y
Again using product rule, the equations are not identical so it is not symmetric about the origin