Q:

How can I plot a paraboloid?

How do I plot a function for a paraboloid? Im putting together surfaces to model lipstick. I need the paraboloid for the top part and then I'll be cutting the paraboloid at angle with another surface. But I can't seem to get a handle on how to plot a simple paraboloid function.

A:

For fun:
RegionPlot3D[
 z <= -2 x^2 - 2 y^2 && z <= 8 x + y - 20,
 {x, -10, 10}, {y, -10, 10}, {z, -100, 0},
 PlotPoints -> 150, Mesh -> None, 
 PlotStyle -> Directive[Darker@Red, Specularity[1]],
 Axes -> False, Boxed -> False
]

