How to recognise geometric symmetry in a formula
Solution 1:
Request from comments:
-
If $z$ can be expressed as a function of $x^2$ and $y^2$ with no other $x$ or $y$ terms then there is reflection symmetry.
-
If $z$ can be expressed purely as a function of $r=\sqrt{x^2+y^2}$ with no $\theta$ or other $x$ or $y$ terms, then it is fully rotationally symmetry about the $z$-axis.
-
It may look like a paraboloid but thanks to the $\frac32$ exponent, it is not one