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 polynomial A complex quadratic polynomial is a quadratic polynomial whose coefficients and variable (mathematics), variable are complex numbers. Properties Quadratic polynomials have the following properties, regardless of the form: *It is a unicritical pol ...

s, 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 In elementary algebra, the quadratic formula is a closed-form expression describing the solutions of a quadratic equation. Other ways of solving quadratic equations, such as completing the square, yield the same solutions. Given a general quadr ...

, 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) In multivariate statistics, if \varepsilon is a vector of n random variables, and \Lambda is an n-dimensional symmetric matrix, then the scalar quantity \varepsilon^T\Lambda\varepsilon is known as a quadratic form in \varepsilon. Expectation It c ...

, scalar quantity ε'Λε for an ''n''-dimensional square matrix *

Quadratic mean In mathematics, the root mean square (abbrev. RMS, or rms) of a set of values is the square root of the set's mean square. Given a set x_i, its RMS is denoted as either x_\mathrm or \mathrm_x. The RMS is also known as the quadratic mean (denoted M ...

, the square root of the mean of the squares of the data *

Quadratic variation In mathematics, quadratic variation is used in the analysis of stochastic processes such as Brownian motion and other martingales. Quadratic variation is just one kind of variation of a process. Definition Suppose that X_t is a real-valued st ...

, 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 mathematical analysis, particularly numerical analysis, the rate of convergence and order of convergence of a sequence that converges to a limit are any of several characterizations of how quickly that sequence approaches its limit. These are ...

, in which the distance to a convergent sequence's limit is squared at each step *

Quadratic differential In mathematics, a quadratic differential on a Riemann surface is a section of the symmetric square of the holomorphic cotangent bundle. If the section is holomorphic, then the quadratic differential is said to be holomorphic. The vector space of h ...

, 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 Quadratic programming (QP) is the process of solving certain mathematical optimization problems involving quadratic functions. Specifically, one seeks to optimize (minimize or maximize) a multivariate quadratic function subject to linear constr ...

, a special type of mathematical optimization problem *

Quadratic growth In mathematics, a function or sequence is said to exhibit quadratic growth when its values are proportional to the square of the function argument or sequence position. "Quadratic growth" often means more generally "quadratic growth in the limi ...

, an asymptotic growth rate proportional to a quadratic function *

Periodic points of complex quadratic mappings This article describes periodic points of some Complex quadratic polynomial, complex quadratic maps. A map is a formula for computing a value of a variable based on its own previous value or values; a Quadratic equation, quadratic map is one that in ...

, 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 Quadratic probing is an open addressing scheme in computer programming for resolving hash collisions in hash tables. Quadratic probing operates by taking the original hash index and adding successive values of an arbitrary quadratic polynomial un ...

, a scheme in computer programming for resolving collisions in hash tables *

Quadratic classifier In statistics, a quadratic classifier is a statistical classifier that uses a quadratic decision surface to separate measurements of two or more classes of objects or events. It is a more general version of the linear classifier. The classific ...

, used in machine learning to separate measurements of two or more classes of objects *

Quadratic time In theoretical computer science, the time complexity is the computational complexity that describes the amount of computer time it takes to run an algorithm. Time complexity is commonly estimated by counting the number of elementary operations p ...

, in referring to algorithms with quadratic time complexity

Other

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