Definitions
from The American Heritage® Dictionary of the English Language, 4th Edition
 adj. Mathematics Of, relating to, or containing quantities of the second degree.
from Wiktionary, Creative Commons Attribution/ShareAlike License
 adj. squareshaped
 adj. of a polynomial, involving the second power (square) of a variable but no higher powers, as .
 adj. of an equation, of the form .
 adj. of a function, of the form .
 n. A quadratic polynomial, function or equation.
from the GNU version of the Collaborative International Dictionary of English
 adj. Of or pertaining to a square, or to squares; resembling a quadrate, or square; square.
 adj. Tetragonal.
 adj. Pertaining to terms of the second degree.
from The Century Dictionary and Cyclopedia
 In algebra, involving the square and no higher power of the unknown quantity or variable of the second degree; of two dimensions.
 In crystallography, tetragonal or dimetric: applied to the system that includes the square prism and related forms. See crystallography.
 n. In algebra, an equation in which the highest power of the unknown quantity is the second, the general form being
 n. plural That branch of algebra which treats of quadratic equations.
from WordNet 3.0 Copyright 2006 by Princeton University. All rights reserved.
 n. a polynomial of the second degree
 n. an equation in which the highest power of an unknown quantity is a square
 adj. of or relating to the second power
 adj. of or relating to or resembling a square
Etymologies
Examples

Then he got out notebook and algebra and lost himself in quadratic equations, while the hours slipped by, and the stars dimmed, and the gray of dawn flooded against his window.

By the way over the small range that you have plotted over a quadratic is a good approximation to an exponential which is exactly what would be expected from the radiative forcing of CO2.

However, the masses of scalar fields receive large corrections from quantum effects (socalled quadratic divergences) and, unless one finetunes the theory a truly ridiculous amount, the expected mass of the Higgs boson may be as high as the Planck scale  sixteen orders of magnitude higher than the weak scale.

The Kerr effect, also called the quadratic electrooptic effect (QEO effect), is a change in the refractive index of a material in response to an applied electric field.

He solved Algebra equations of the first and second degree (known as quadratic equations, and are are prevelant in science and engineering) and also introduced the geometrical method of solving these equations.

This is most commonly found in the industry and sometimes is known as a quadratic torque load.

By completing the square on a general quadratic equation in standard form we come up with what is called the quadratic formula.

is called a quadratic expression in x. is called a quadratic equation in x.

Furthermore, it is admitted that never, never, in a million lifetimes, could Michael have demonstrated a proposition in Euclid or solved a quadratic equation.

Kingsolver reported a median absolute value of 0.16 for linear selection, and a median absolute value of 0.10 for quadratic selection.
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