In mathematics, the term quadratic describes something that pertains to

squares In geometry, a square is a regular polygon, regular quadrilateral. It has four straight sides of equal length and four equal angles. Squares are special cases of rectangles, which have four equal angles, and of rhombuses, which have four equal si ...

, to the operation of squaring, to terms of the second degree, or equations or formulas that involve such terms. ''Quadratus'' is

Latin Latin ( or ) is a classical language belonging to the Italic languages, Italic branch of the Indo-European languages. Latin was originally spoken by the Latins (Italic tribe), Latins in Latium (now known as Lazio), the lower Tiber area aroun ...

for ''square''.

Mathematics

Algebra (elementary and abstract)

Quadratic function In mathematics, a quadratic function of a single variable (mathematics), variable is a function (mathematics), function of the form :f(x)=ax^2+bx+c,\quad a \ne 0, where is its variable, and , , and are coefficients. The mathematical expression, e ...

(or quadratic polynomial), a polynomial function that contains terms of at most second degree ** Complex quadratic polynomials, are particularly interesting for their sometimes chaotic properties under iteration *

Quadratic equation In mathematics, a quadratic equation () is an equation that can be rearranged in standard form as ax^2 + bx + c = 0\,, where the variable (mathematics), variable represents an unknown number, and , , and represent known numbers, where . (If and ...

, a polynomial equation of degree 2 (reducible to 0 = ''ax''² + ''bx'' + ''c'') * Quadratic formula, calculation to solve a quadratic equation for the independent variable (''x'') *

Quadratic field In algebraic number theory, a quadratic field is an algebraic number field of Degree of a field extension, degree two over \mathbf, the rational numbers. Every such quadratic field is some \mathbf(\sqrt) where d is a (uniquely defined) square-free ...

, an algebraic number field of degree two over the field of rational numbers *

Quadratic irrational In mathematics, a quadratic irrational number (also known as a quadratic irrational or quadratic surd) is an irrational number that is the solution to some quadratic equation with rational coefficients which is irreducible over the rational numb ...

or "quadratic surd", an irrational number that is a root of a quadratic polynomial

Calculus

* Quadratic integral, the integral of the reciprocal of a second-degree polynomial

Statistics and stochastics

* Quadratic form (statistics), scalar quantity ε'Λε for an ''n''-dimensional square matrix * Quadratic mean, the square root of the mean of the squares of the data * Quadratic variation, in stochastics, useful for the analysis of Brownian motion and martingales

Number theory

Quadratic reciprocity In number theory, the law of quadratic reciprocity is a theorem about modular arithmetic that gives conditions for the solvability of quadratic equations modulo prime numbers. Due to its subtlety, it has many formulations, but the most standard st ...

, a theorem from number theory *

Quadratic residue In number theory, an integer ''q'' is a quadratic residue modulo operation, modulo ''n'' if it is Congruence relation, congruent to a Square number, perfect square modulo ''n''; that is, if there exists an integer ''x'' such that :x^2\equiv q \pm ...

, an integer that is a square modulo ''n'' * Quadratic sieve, a modern integer factorization algorithm

Other mathematics

* Quadratic convergence, in which the distance to a convergent sequence's limit is squared at each step * Quadratic differential, a form on a Riemann surface that locally looks like the square of an abelian differential *

Quadratic form In mathematics, a quadratic form is a polynomial with terms all of degree two (" form" is another name for a homogeneous polynomial). For example, 4x^2 + 2xy - 3y^2 is a quadratic form in the variables and . The coefficients usually belong t ...

, a homogeneous polynomial of degree two in any number of variables * Quadratic programming, a special type of mathematical optimization problem * Quadratic growth, an asymptotic growth rate proportional to a quadratic function * Periodic points of complex quadratic mappings, a type of graph that can be used to explore stability in control systems * Quadratic Bézier curve, a type of Bézier curve

Computer science

* Quadratic probing, a scheme in computer programming for resolving collisions in hash tables * Quadratic classifier, used in machine learning to separate measurements of two or more classes of objects * Quadratic time, in referring to algorithms with quadratic time complexity

Other

* ''Quadratic'' (collection), a 1953 collection of science fiction novels by Olaf Stapledon and Murray Leinster