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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 quadratic form is a polynomial with terms all of degree two ... a quadratic form on V is a function Q : V → K that has the following property: ...
Abū Kāmil Shujā ibn Aslam (Egypt, 10th century) in particular was the first to accept irrational numbers (often in the form of a square root, cube root or fourth root) as solutions to quadratic equations or as coefficients in an equation. [30] The 9th century Indian mathematician Sridhara wrote down rules for solving quadratic equations. [31]
Quadratic forms correspond one-to-one to symmetric bilinear forms over the same space. [2] A symmetric bilinear form is also described as definite, semidefinite, etc. according to its associated quadratic form. A quadratic form Q and its associated symmetric bilinear form B are related by the following equations:
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.
The derivative of a quartic function is a cubic function. Sometimes the term biquadratic is used instead of quartic, but, usually, biquadratic function refers to a quadratic function of a square (or, equivalently, to the function defined by a quartic polynomial without terms of odd degree), having the form
The quadratic equation on a number can be solved using the well-known quadratic formula, which can be derived by completing the square. That formula always gives the roots of the quadratic equation, but the solutions are expressed in a form that often involves a quadratic irrational number, which is an algebraic fraction that can be evaluated ...
Quadratic polynomials have the following properties, regardless of the form: It is a unicritical polynomial, i.e. it has one finite critical point in the complex plane, Dynamical plane consist of maximally 2 basins: basin of infinity and basin of finite critical point ( if finite critical point do not escapes)