Definitions
from The American Heritage® Dictionary of the English Language, 4th Edition
 n. A surface having parabolic sections parallel to a single coordinate axis and elliptic sections perpendicular to that axis.
from Wiktionary, Creative Commons Attribution/ShareAlike License
 n. A surface having a parabolic cross section parallel to an axis, and circular or elliptical cross section perpendicular to the axis; especially the surface of revolution of a parabola.
from the GNU version of the Collaborative International Dictionary of English
 n. 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.
from The Century Dictionary and Cyclopedia
 n. A solid or surface of the second degree some of whose planesections are parabolas.
 Paraboloidal.
 n. The solid generated by the revolution of a parabola about its axis; a parabolic conoid.
 n. A curve whose equation is of the form ax = y.
from WordNet 3.0 Copyright 2006 by Princeton University. All rights reserved.
 n. a surface having parabolic sections parallel to a single coordinate axis and elliptic sections perpendicular to that axis
Etymologies
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Examples

A paraboloid is a threedimensional shape that has two terms of x, y, or z that are squared and one term of x, y, or z that is not.

When one squared term is negative and one is positive, like in the second equation, the paraboloid is a hyperbolic paraboloid (shaped like a saddle When both squared terms are positive, like in the first equation, the paraboloid is an

We're back to my hyperbolic, paraboloid, transitional floating zone.

If you aren't quite sure what a hyperbolic paraboloid is, it's a mathematical term to describe a surface shaped like a saddle.

"Geometrically, it's a hyperbolic paraboloid, but that's not very sexy."

Gaudi, of course, is the leading genius: his structural experiments took off from Catalan Gothic to produce amazing paraboloid arches; his rich details of fauna and flora in iron, stone or wildly colorful bits of tile drew on the work of the best Catalonian craftsmen.

It has 4 nester hyperboloid mirrors and 4 nested paraboloid mirrors to focus the xrays.

It is not the scope of the synagogue that sets it apart, or the technical marvel of his hallmark hyperbolic paraboloid roofs — which he describes as being shaped something like a Pringles potato chip.

The saddleshaped structure is also known as a hyperbolic paraboloid surface, or an anticlastic surface.

And interestingly, this turns out  the stomatopod saddle turns out to be the first described biological hyperbolic paraboloid spring.
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