In mathematics, the term quadratic describes something that pertains to

squares In Euclidean geometry, a square is a regular quadrilateral, which means that it has four equal sides and four equal angles (90-degree angles, π/2 radian angles, or right angles). It can also be defined as a rectangle with two equal-length adj ...

, to the operation of squaring, to terms of the second

degree Degree may refer to: As a unit of measurement * Degree (angle), a unit of angle measurement ** Degree of geographical latitude ** Degree of geographical longitude * Degree symbol (°), a notation used in science, engineering, and mathematics ...

, or equations or formulas that involve such terms. ''Quadratus'' is

Latin Latin (, or , ) is a classical language belonging to the Italic branch of the Indo-European languages. Latin was originally a dialect spoken in the lower Tiber area (then known as Latium) around present-day Rome, but through the power of the ...

for ''square''.

Mathematics

Algebra (elementary and abstract)

Quadratic function In mathematics, a quadratic polynomial is a polynomial of degree two in one or more variables. A quadratic function is the polynomial function defined by a quadratic polynomial. Before 20th century, the distinction was unclear between a polynomial ...

(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 are complex numbers. Properties Quadratic polynomials have the following properties, regardless of the form: *It is a unicritical polynomial, i.e. it has one ...

s, are particularly interesting for their sometimes chaotic properties under iteration *

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

, a polynomial equation of degree 2 (reducible to 0 = ''ax''² + ''bx'' + ''c'') *

Quadratic formula In elementary algebra, the quadratic formula is a formula that provides the solution(s) to a quadratic equation. There are other ways of solving a quadratic equation instead of using the quadratic formula, such as factoring (direct factoring, gr ...

, 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 two over \mathbf, the rational numbers. Every such quadratic field is some \mathbf(\sqrt) where d is a (uniquely defined) square-free integer different from 0 an ...

, 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, a quadratic irrationality or quadratic surd) is an irrational number that is the solution to some quadratic equation with rational coefficients which is irreducible ...

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 ...

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

Quadratic mean In mathematics and its applications, the root mean square of a set of numbers x_i (abbreviated as RMS, or rms and denoted in formulas as either x_\mathrm or \mathrm_x) is defined as the square root of the mean square (the arithmetic mean of the ...

, 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 sto ...

, 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 called a quadratic residue modulo ''n'' if it is congruent to a perfect square modulo ''n''; i.e., if there exists an integer ''x'' such that: :x^2\equiv q \pmod. Otherwise, ''q'' is called a quadratic no ...

, an integer that is a square modulo ''n'' *

Quadratic sieve The quadratic sieve algorithm (QS) is an integer factorization algorithm and, in practice, the second fastest method known (after the general number field sieve). It is still the fastest for integers under 100 decimal digits or so, and is considerab ...

, a modern integer factorization algorithm

Other mathematics

Quadratic convergence In numerical analysis, the order of convergence and the rate of convergence of a convergent sequence are quantities that represent how quickly the sequence approaches its limit. A sequence (x_n) that converges to x^* is said to have ''order of co ...

, 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 ho ...

, a form on a Riemann surface that locally looks like the square of an

abelian differential In mathematics, ''differential of the first kind'' is a traditional term used in the theories of Riemann surfaces (more generally, complex manifolds) and algebraic curves (more generally, algebraic varieties), for everywhere-regular differential 1 ...

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 to a ...

, 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 constra ...

, 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 limit", ...

, an asymptotic growth rate proportional to a quadratic function *

Periodic points of complex quadratic mappings This article describes periodic points of some 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 map is one that involves the previous value raised to the powers o ...

, a type of graph that can be used to explore stability in control systems * Quadratic bézier curve, a type of bezier 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 unti ...

, 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 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 performed by t ...

, in referring to algorithms with quadratic time complexity

Other

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