quadratic

English

polynomial degrees

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Next:	cubic

Alternative forms

• quadratick (obsolete)

Etymology

From French quadratique (1765), from Latin quadrātus + -ique (English -ic), form of quadrō (“I make square”), from quādrus (“square”), ultimately from Proto-Indo-European *kʷetwóres (“four”), whence also Latin quartus (“fourth”).

Pronunciation

• IPA^(key): /kwɒdˈɹætɪk/, /kwəˈdɹætɪk/

• Audio (Southern England):

  (file)

Adjective

quadratic (not comparable)

1. Square-shaped.
2. (mathematics) Of a polynomial, equation or function, second-degree: involving the second power (square) of a variable but no higher powers, as $ax^{2}+bx+c$.
   • 2015 November 17, “Fast Fragmentation of Networks Using Module-Based Attacks”, in PLOS ONE‎^[1], →DOI:

     A linear or even a quadratic relation between the overall gain in efficiency η and the modularity Q would have been easily explained through S1 Fig, which shows a quadratic (inverse) relation between interedges fraction and modularity.

Translations

of a class of polynomial of the form y = ax² + bx + c

• Armenian: քառակուսի (hy) (kʻaṙakusi)
• Azerbaijani: kvadratik
• Belarusian: квадратны (kvadratny)
• Bulgarian: квадратен (kvadraten)
• Catalan: quadràtic
• Chinese:

  Mandarin: 二次 (zh) (èrcì)

• Czech: kvadratický
• Dutch: kwadratisch (nl)
• Esperanto: kvadrata
• Finnish: toisen asteen (literally “of the second degree”)
• French: quadratique (fr) m or f
• Georgian: კვადრატული (ḳvadraṭuli)
• German: quadratisch (de)
• Greek: τετραγωνικός (el) m (tetragonikós), τετραγωνική (el) f (tetragonikí), τετραγωνικό (el) n (tetragonikó)
• Hindi: द्विघात (dvighāt)
• Indonesian: kuadratik, kuadratis
• Italian: quadratico (it) m, quadratica f
• Japanese: 二次 (ja) (niji)
• Kazakh: шаршы (şarşy)
• Khmer: ដឺក្រេទីពីរ (dəɨkrei tii pii)
• Korean: 이차(二次) (icha)
• Kyrgyz: чарчы (ky) (carcı)
• Malay: kuadratik (ms)
• Portuguese: quadrático (pt)
• Russian: квадра́тный (ru) (kvadrátnyj)
• Scottish Gaelic: ceàrnach
• Spanish: cuadrático
• Swedish: kvadratisk (sv), andragrads-, andragradspolynom (sv)
• Uzbek: kvadratik

Noun

quadratic (plural quadratics)

1. (mathematics) A quadratic polynomial, function or equation.
   • 1809, Charles Hutton, The Philosophical Transactions of the Royal Society of London from Their Commencement in 1665 to the Year 1800, volume 3, page 41:

     If the binomial roots of a series of quadratics be squaredly squared, and those results be constant portions of the cube of the resolvend, and the dioristic limit; […]

Translations

quadratic polynomial

• Chinese:

  Mandarin: 二次式 (zh)

• Finnish: toisen asteen polynomi (literally “polynomial of the second degree”)
• Japanese: 二次式
• Maori: whārite pūrua (referring to an equation)

Usage notes

Not to be confused with quartic (“degree four”). Both derive ultimately from Proto-Indo-European *kʷetwóres (“four”), with quadratic coming from “four-sided”, hence “square, two-dimensional, degree two”.

Derived terms

• quadratic equation
• quadratic field
• quadratic form
• quadratic formula
• quadratic function
• quadratic integer
• quadratic mean
• quadratic reciprocity
• quadratic residue
• quadratic surd
• quadratic time

Related terms

• quadrate
• quadrature

See also

• square

Further reading

• “quadratic”, in Webster’s Revised Unabridged Dictionary, Springfield, Mass.: G. & C. Merriam, 1913, →OCLC.
• “quadratic”, in The Century Dictionary […], New York, N.Y.: The Century Co., 1911, →OCLC.
• “quadratic”, in OneLook Dictionary Search.