The solid generated by the rotation of a parabola about its axis; any surface of the second order whose sections by planes parallel to a given line are parabolas.

A geometric surface whose sections parallel to two co-ordinate planes are parabolic and whose sections parallel to the third plane are either elliptical or hyperbolic.

a surface having parabolic sections parallel to a single coordinate axis and elliptic sections perpendicular to that axis

a three dimensional shape whose cross-sectional shape is a parabola (just like the cross-section of a geodesic dome would be a circular arc)

Take a parabola and rotate it around its origin (the "bottom" of the curve) and you get a paraboloid. In other words, a paraboloid is a 3-dimensional parabola. A Newtonian style telescope mirror has a paraboloidal (not a parabolic) shape.

(Or equilibrium paraboloid.) The geometrical figure obtained by rotating a parabola about its axis. In experimental meteorology and oceanography such a figure is sometimes used as the lower boundary of a model atmosphere or ocean, and is especially important because, at a proper rotation rate, it is an equipotential surface for apparent gravity in the model. If ω is the rotation rate of the apparatus, the acceleration of local earth's gravity, the coordinate parallel to the vertical rotation axis, and the radial coordinate, an equilibrium paraboloid is given by This surface is the laboratory equivalent of the spheroidal equipotential surfaces of the earth's apparent gravity field.

A parabola of revolution. Classical shape of a satellite antenna's reflector.