What does quadratic mean?
Quadratic is most often used as a mathematical adjective for an expression, equation, function, or curve involving a term of the second degree, such as x squared. It also functions as a noun for a second-degree polynomial equation, especially one written in the form ax squared plus bx plus c equals zero. Such equations can be solved with the quadratic formula. Although the common sense is mathematical, quadratic also has a geometrical meaning: square-shaped or having four equal sides. The mathematical sense comes from the Latin word for square, reflecting the term's long history in geometry. In general use, quadratic suggests curvature or an accelerating rate rather than the straight, constant relationship described as linear. Knowing the word is useful in algebra, physics, statistics, engineering, and computer graphics, where second-degree relationships are common and often require special handling.
In mathematics, involving the second degree or a term of the second power. In geometry, square-shaped or having four equal sides.
"The equation contains one quadratic term."
The mathematical sense is overwhelmingly dominant; the geometrical sense is rare and formal.
A polynomial, function, or equation of the second degree, especially a quadratic equation.
"She solved the quadratic and checked both possible roots."
As a noun, quadratic usually means a quadratic equation, though context may instead indicate a quadratic function or polynomial.
The plural is grammatically possible but uncommon; writers usually specify “quadratic equations” when that is the intended meaning.
"The program solved three quadratics before checking the results."
Quadratic hides a four in plain sight: it descends from the Latin word for a square, a shape with four equal sides.
Reviewed by Deb Chak, Editor. AI-assisted content curated by RJS Tech Solutions LLP.
Where does quadratic come from?
English borrowed quadratic by the 17th century from New Latin quadraticus, a derivative of Latin quadratus, meaning “square.” Latin quadratus was associated with quadri-, the form of “four” used in compounds, so its literal connection is to a square figure with four equal sides. Its English relatives include quadrant, quadrangle, quadruple, and square.
Related word forms
How quadratic is actually used
The mathematical senses are overwhelmingly dominant in modern English. The geometrical sense meaning square-shaped is comparatively rare and formal; as a noun, quadratic usually refers to a quadratic equation but may also denote a quadratic function or polynomial.
Easily confused with quadratic
A quadratic is a degree-two expression, function, or equation, whereas quadrature is the process or result of finding the area of a square or a related mathematical measure.