Definitions
from The American Heritage® Dictionary of the English Language, 4th Edition
 n. A plane curve formed by the intersection of a right circular cone and a plane parallel to an element of the cone or by the locus of points equidistant from a fixed line and a fixed point not on the line.
from Wiktionary, Creative Commons Attribution/ShareAlike License
 n. The conic section formed by the intersection of a cone with a plane parallel to a tangent plane to the cone; the locus of points equidistant from a fixed point (the focus) and line (the directrix).
 n. The explicit drawing of a parallel between two essentially dissimilar things, especially with a moral or didactic purpose. A parable.
from the GNU version of the Collaborative International Dictionary of English
 n. A kind of curve; one of the conic sections formed by the intersection of the surface of a cone with a plane parallel to one of its sides. It is a curve, any point of which is equally distant from a fixed point, called the focus, and a fixed straight line, called the directrix. See focus.
 n. One of a group of curves defined by the equation y = axn where n is a positive whole number or a positive fraction. For the cubical parabola n = 3; for the semicubical parabola n = 3/2. See under cubical, and semicubical. The parabolas have infinite branches, but no rectilineal asymptotes.
from The Century Dictionary and Cyclopedia
 n. Same as parabole.
 n. A curve commonly defined as the intersection of a cone with a Plane parallel with its side.
 n. By extension, any algebraical curve, or branch of a curve, having the line at infinity as a real tangent.
from WordNet 3.0 Copyright 2006 by Princeton University. All rights reserved.
 n. a plane curve formed by the intersection of a right circular cone and a plane parallel to an element of the curve
Etymologies
Examples

Terrified of boys and the showers … especially since I have actually witnessed one myself. barely missed me and the parabola is impressive.

Ms. Drugge, my 8th grade math teacher, was explaining that the model we were dissecting was called a parabola.

For example, Archimedes proved that the area of a section of a parabola is fourthirds the area of the triangle inside it (shown in red in the diagram below).

She smiled again – brutally, we thought – described a significant parabola from the mouth outwards with her hand, raised her eyebrows, and asked us something in Catalan.

The arching curve above  technically known as a "parabola"  is the signature of the squaring function x2 operating behind the scenes.

Claim someone shot out the indow of your Congressoinal office when it was really just a satellite office, happened at like 1 or 2 a.m., the trajectory of th ebullet meant the shooter was either wearing the baloonboy balloon and shooting from above or such a superb marksman he could aim a bullet's parabola from the ground while firing straight up, and IT WASN'T EVEN A WINDOW TO THE OFFICE SPACE YOU WERE RENTING, BUT A NEARBY WINDOW IN THE SAME BUILDING.

See, it's just not okay to be calling a parabola a sphere.

“My friend,” answered the captain, “the parabola is a curve of the second order, the result of the section of a cone intersected by a plane parallel to one of the sides.”

In this case, the parabola is the graph of the function.

The former involves the conception of a circular directrix with a ratio equal to unity in all cases; and the two definitions become identical in the construction of the parabola, which is in fact the only curve of which a clear idea is given by either of them.
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