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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.)
Quadratic formula. The roots of the quadratic function y = 1 2 x2 − 3x + 5 2 are the places where the graph intersects the x -axis, the values x = 1 and x = 5. They can be found via the quadratic formula. In elementary algebra, the quadratic formula is a closed-form expression describing the solutions of a quadratic equation.
Problems of this type included finding the dimensions of a rectangle given its area and the amount by which the length exceeds the width. Tables of values of n 3 + n 2 were used to solve certain cubic equations. For example, consider the equation: + =. Multiplying the equation by a 2 and dividing by b 3 gives:
The graph of a univariate quadratic function is a parabola, a curve that has an axis of symmetry parallel to the y -axis. If a quadratic function is equated with zero, then the result is a quadratic equation. The solutions of a quadratic equation are the zeros of the corresponding quadratic function. The bivariate case in terms of variables x ...
The rate of convergence is distinguished from the number of iterations required to reach a given accuracy. For example, the function f(x) = x 20 − 1 has a root at 1. Since f ′(1) ≠ 0 and f is smooth, it is known that any Newton iteration convergent to 1 will converge quadratically. However, if initialized at 0.5, the first few iterates of ...
A Bézier curve is defined by a set of control points P0 through Pn, where n is called the order of the curve (n = 1 for linear, 2 for quadratic, 3 for cubic, etc.). The first and last control points are always the endpoints of the curve; however, the intermediate control points generally do not lie on the curve.
In mathematics, a quartic equation is one which can be expressed as a quartic function equaling zero. The general form of a quartic equation is. Graph of a polynomial function of degree 4, with its 4 roots and 3 critical points. where a ≠ 0. The quartic is the highest order polynomial equation that can be solved by radicals in the general ...
t. e. Okun's law in macroeconomics states that in an economy the GDP growth should depend linearly on the changes in the unemployment rate. Here the ordinary least squares method is used to construct the regression line describing this law. In statistics, ordinary least squares (OLS) is a type of linear least squares method for choosing the ...