$f(x, y) = -x^2-y^2+4$ is the equation of a paraboloid which sits on the XY plane and protrudes toward Z-axis.
So, if I want a paraboloid to be drawn on the surface XZ, I should write: $f(x, z) = -x^2-z^2+4$
My question is, is it possible to write an equation of a paraboloid as a function of x,y, even though it sits on the surface XZ?
Why or why not?