Paraboloid

Paraboloid is the surface of revolution of the curve parabola

paraboloid xMhhC
paraboloid 
ParametricPlot3D[{u, v, (u*u + v*v)}, {u, -1, 1}, {v, -1, 1},
 PlotStyle ->
  Directive[RandomColor[], Opacity[.8], Specularity[1, 20]]]
paraboloid 77462
paraboloid 
ParametricPlot3D[{u, v, (u*u + v*v)}, {u, -10, 10}, {v, -10, 10},
 PlotPoints -> {400, 400},
 PlotStyle ->
  Directive[RandomColor[], Opacity[.7], Specularity[1, 20]],
 RegionFunction -> Function[{x, y, z}, 0 < x^2 + y^2 + z^2 < 5],
 Axes -> False, Boxed -> False
 ]
paraboloid DtwHp
paraboloid 
ContourPlot3D[z == x^2/1 + y^2/1, {x, -2, 2}, {y, -2, 2}, {z, 0, 3},
 PlotRange -> {{-2, 2}, {-2, 2}, {0, 2}},
 PlotPoints -> 40, Boxed -> False, Axes -> False,
 BoxRatios -> Automatic,
 ContourStyle ->
  Directive[RandomColor[], Opacity[0.7], Specularity[White, 30]]]

Conic Section Surfaces