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 (“to 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 $a{x}^2+bx+c$.
   • 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)
• Georgian: კვადრატული (ḳvadraṭuli)
• German: quadratisch (de)
• Greek: τετραγωνικός (el) (tetragonikós)
• Hindi: द्विघात (dvighāt)
• Indonesian: kuadratik, kuadratis
• Italian: quadratico (it)
• Japanese: 二次 (ja) (niji)
• Kazakh: шаршы (šaršı)
• Khmer: ដឺក្រេទីពីរ (dəɨkrei tii pii)
• Korean: 이차(二次) (icha)
• Kyrgyz: чарчы (ky) (carcı)
• Latin: quadrāticus
• Malay: kuadratik (ms)
• Polish: kwadratowy (pl)
• 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, The Royal Society of London for Improving Natural Knowledge, 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

• Bulgarian: квадратен тричлен m (kvadraten tričlen), квадратен полином m (kvadraten polinom), квадратична функция f (kvadratična funkcija), квадратно уравнение n (kvadratno uravnenie)
• Chinese:

  Mandarin: 二次式 (zh)

• Finnish: toisen asteen polynomi (literally “polynomial of the second degree”)
• Japanese: 二次式
• Latin: quadrāticum n
• Māori: 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

• biquadratic
• multiquadratic
• nonquadratic
• paraquadratic
• polyquadratic
• postquadratic
• prequadratic
• quadratic acid
• quadratically
• quadratic equation
• quadratic field
• quadratic form
• quadratic formula
• quadratic function
• quadratic integer
• quadraticity
• quadratic mean
• quadratic reciprocity
• quadratic residue
• quadratic surd
• quadratic time
• quadratization
• quadratize
• subquadratic
• superquadratic

Related terms

• quadrate
• quadrature

See also

• square

Further reading

• “quadratic”, in Webster’s Revised Unabridged Dictionary, Springfield, Mass.: G. & C. Merriam, 1913, →OCLC.
• William Dwight Whitney, Benjamin Eli Smith, editors (1895–1910), “quadratic”, in The Century Dictionary […], New York, N.Y.: The Century Co., →OCLC.
• “quadratic”, in OneLook Dictionary Search.