TrueType fonts use Bézier splines composed of quadratic Bézier curves.

A quadratic Bézier curve is also a parabolic segment.

Writing B < sub > P < sub > i </ sub >, P < sub > j </ sub >, P < sub > k </ sub ></ sub >( t ) for the quadratic Bézier curve defined by points P < sub > i </ sub >, P < sub > j </ sub >, and P < sub > k </ sub >, the cubic Bézier curve can be defined as a linear combination of two quadratic Bézier curves:

* Every quadratic Bézier curve is also a cubic Bézier curve, and more generally, every degree n Bézier curve is also a degree m curve for any m > n. In detail, a degree n curve with control points P < sub > 0 </ sub >, …, P < sub > n </ sub > is equivalent ( including the parametrization ) to the degree n + 1 curve with control points P '< sub > 0 </ sub >, …, P '< sub > n + 1 </ sub >, where.

A Bézier triangle is a special type of Bézier surface, which is created by ( linear, quadratic, cubic or higher degree ) interpolation of control points.

File: Circle and quadratic bezier. svg | Eight-segment quadratic Bézier spline ( red ) approximating a circle ( black ) with control points

* a curve shape was a single quadratic Bézier curve defined by three control points.

* a path shape which was a sequence of quadratic Bézier curves.

But if no two lines of the regulus of multiple secants of **zg can intersect, then the regulus must be quadratic, or in other words, **zg must be either a Af or a Af curve on a nonsingular quadric surface.

The red curve is the initial state at time zero at which the string is " let free " in a predefined shape The initial state for " Investigation by numerical methods " is set with quadratic splines as follows:

Following von Koch's concept, several variants of the Koch curve were designed, considering right angles ( quadratic ), other angles ( Césaro ) or circles and their extensions to higher dimensions ( Sphereflake ):

This is a quadratic form in the tangent plane to the surface at a point whose value at a particular tangent vector X to the surface is the normal component of the acceleration of a curve along the surface tangent to X ; that is, it is the normal curvature to a curve tangent to X ( see above ).

However, wherever a minimum occurs in the dispersion relation, the minimum can be approximated by a quadratic curve in the small region around that minimum, for example:

The integrand is the restriction to the curve of the square root of the ( quadratic ) differential

Six terms will be needed to vanish a quadratic curve and so on given the other constraints to be included.

It can be parameterized by drawing a line with slope t through the rational point, and intersection with the plane quadratic curve ; this gives a polynomial with F-rational coefficients and one F-rational root, hence the other root is F-rational ( i. e., belongs to F ) also.

with rational coefficients must satisfy the simple quadratic curve

An accelerating or decelerating rate of response would lead to a quadratic ( or similar ) curve.

In mathematics, a degenerate conic is a conic ( degree-2 plane curve, the zeros of a degree-2 polynomial equation, a quadratic ) that fails to be an irreducible curve.

The most obvious of these is the quadratic complex of tangents to Q, each line of which is transformed into the entire pencil of lines tangent to Q at the image of the point of tangency of the given line.

If the quadratic polynomial is monic then the roots are quadratic integers.

The case where X is F, and we have a bilinear form, is particularly useful ( see for example scalar product, inner product and quadratic form ).

As a parabola is a conic section, some sources refer to quadratic Béziers as " conic arcs ".

One of these, Itō's lemma, expresses the composite of an Itō process ( or more generally a semimartingale ) dX < sub > t </ sub > with a twice-differentiable function f. In Itō's lemma, the derivative of the composite function depends not only on dX < sub > t </ sub > and the derivative of f but also on the second derivative of f. The dependence on the second derivative is a consequence of the non-zero quadratic variation of the stochastic process, which broadly speaking means that the process can move up and down in a very rough way.

The set of constructible numbers can be completely characterized in the language of field theory: the constructible numbers form the quadratic closure of the rational numbers: the smallest field extension of which is closed under square root and complex conjugation.

This is a quadratic equation which we can solve.

There is no evidence that suggests Diophantus even realized that there could be two solutions to a quadratic equation.

Formulas for the eccentricity of an ellipse that is expressed in the more general quadratic form are described in the article dedicated to conic sections.

The Earley parser executes in cubic time in the general case, where n is the length of the parsed string, quadratic time for unambiguous grammars, and linear time for almost all LR ( k ) grammars.

A quadratic equation is one which includes a term with an exponent of 2, for example,, and no term with higher exponent.

In general, a quadratic equation can be expressed in the form, where is not zero ( if it were zero, then the equation would not be quadratic but linear ).

Because of this a quadratic equation must contain the term, which is known as the quadratic term.

A geometric algebra is the Clifford algebra of a vector space over the field of real numbers endowed with a quadratic form.

Given a finite dimensional real quadratic space with quadratic form, the geometric algebra for this quadratic space is the Clifford algebra Cℓ ( V, Q ).

Marc van Kreveld suggested the algorithmic problem of computing shortest paths between vertices in a line arrangement, where the paths are restricted to follow the edges of the arrangement, more quickly than the quadratic time that it would take to apply a shortest path algorithm to the whole arrangement graph.

He discovered that the so-called Weil representation, previously introduced in quantum mechanics by Irving Segal and Shale, gave a contemporary framework for understanding the classical theory of quadratic forms.

However, it seems that many of the methods for solving linear and quadratic equations used by Diophantus go back to Babylonian mathematics.

Solving this, by a process known as completing the square, leads to the quadratic formula

The Legendre symbol was introduced by Adrien-Marie Legendre in 1798 in the course of his attempts at proving the law of quadratic reciprocity.

Under this state, allele ( gamete ) frequencies can be converted to genotype ( zygote ) frequencies by expanding an appropriate quadratic equation, as shown by Sir Ronald Fisher in his establishment of quantitative genetics.

If the areas of the two parallel faces are A < sub > 1 </ sub > and A < sub > 3 </ sub >, the cross-sectional area of the intersection of the prismatoid with a plane midway between the two parallel faces is A < sub > 2 </ sub >, and the height ( the distance between the two parallel faces ) is h, then the volume of the prismatoid is given by ( This formula follows immediately by integrating the area parallel to the two planes of vertices by Simpson's rule, since that rule is exact for integration of polynomials of degree up to 3, and in this case the area is at most a quadratic in the height.

Methods related to the quadratic sieve approach for integer factorization may be used to collect relations between prime numbers in the number field generated by √ n, and to combine these relations to find a product representation of this type.

Hallgren's algorithm, which can be interpreted as an algorithm for finding the group of units of a real quadratic number field, was extended to more general fields by.

For instance, one could define a general quadratic function by defining

Quadratic equations can be solved by factoring, completing the square, graphing, Newton's method, and using the quadratic formula ( given below ).

The first section of this article does not use the Legendre symbol and gives the formulations of quadratic reciprocity found by Legendre and Gauss.

In computer typography, modern outline fonts describe printable characters ( glyphs ) by cubic or quadratic mathematical curves with control points.

Speeds much higher than the average speed were suppressed by the fact that kinetic energy is quadratic — doubling the speed requires four times the energy — thus the number of atoms occupying high energy modes ( high speeds ) quickly drops off because the constant, equal partition can excite successively fewer atoms.

Zhu also found square and cube roots by solving quadratic and cubic equations, and added to the understanding of series and progressions, classifying them according to the coefficients of the Pascal triangle.

A related programming problem, quadratically constrained quadratic programming, can be posed by adding quadratic constraints on the variables.

Specifically, a Clifford algebra is a unital associative algebra which contains and is generated by a vector space V equipped with a quadratic form Q.

The Clifford algebra Cℓ ( V, Q ) is the " freest " algebra generated by V subject to the condition < ref > Mathematicians who work with real Clifford algebras and prefer positive definite quadratic forms ( especially those working in index theory ) sometimes use a different choice of sign in the fundamental Clifford identity.