A curve is symmetrical about the x-axis if you replace y by -y in the equation

and arrive at the original equation. Here you get -y=3x ²-10 giving y=10-3x ² which is not

the same as y=3x ²-10, so curve is not symmetrical about the x-axis.

A curve is symmetrical about the y-axis if you replace x by -x and arrive at the original equation.

Here y=3(-x)²-10=3x²-10 so curve is symmetrical about the y-axis.

A curve has point symmetry about the origin (0,0) if you replace x by -x and y by -y

and arrive at the original equation. Here, (-y)=3(-x)²-10 giving y=10-3x² which is different

from y=3x ² -10.

If you graph the curve y=3x²-10 you can verify the above.