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Quadratic equation. In mathematics, a quadratic equation (from Latin quadratus ' square ') is an equation that can be rearranged in standard form as [1] where x represents an unknown value, and a, b, and c represent known numbers, where a ≠ 0. (If a = 0 and b ≠ 0 then the equation is linear, not quadratic.)
Application: The 2-points–2-tangents property can be used for the construction of the tangent of a parabola at point , if , and the tangent at are given. Remark 1: The 2-points–2-tangents property of a parabola is an affine version of the 3-point degeneration of Pascal's theorem.
Arc length s of a logarithmic spiral as a function of its parameter θ. Arc length is the distance between two points along a section of a curve. Determining the length of an irregular arc segment by approximating the arc segment as connected (straight) line segments is also called curve rectification.
Quadratic function. In mathematics, a quadratic function of a single variable is a function of the form [1] where is its variable, and , , and are coefficients. The expression , especially when treated as an object in itself rather than as a function, is a quadratic polynomial, a polynomial of degree two.
In mathematics, a parametric equation defines a group of quantities as functions of one or more independent variables called parameters. [1] Parametric equations are commonly used to express the coordinates of the points that make up a geometric object such as a curve or surface, called a parametric curve and parametric surface, respectively.
Curve fitting[1][2] is the process of constructing a curve, or mathematical function, that has the best fit to a series of data points, [3] possibly subject to constraints. [4][5] Curve fitting can involve either interpolation, [6][7] where an exact fit to the data is required, or smoothing, [8][9] in which a "smooth" function is constructed ...
A parabolic segment is the region bounded by a parabola and line. To find the area of a parabolic segment, Archimedes considers a certain inscribed triangle. The base of this triangle is the given chord of the parabola, and the third vertex is the point on the parabola such that the tangent to the parabola at that point is parallel to the chord.
Successive parabolic interpolation is a technique for finding the extremum (minimum or maximum) of a continuous unimodal function by successively fitting parabolas (polynomials of degree two) to a function of one variable at three unique points or, in general, a function of n variables at 1+n(n+3)/2 points, and at each iteration replacing the "oldest" point with the extremum of the fitted ...