Quadratic function: Difference between revisions

Revision as of 00:55, 14 October 2022

Revision as of 15:13, 28 October 2022

Line 1:

{{Short description|Polynomial function of degree two}}

{{for|the zeros of a quadratic function|Quadratic equation|Quadratic formula}}

In [[algebra]], a '''quadratic function''', a '''quadratic polynomial''', a '''polynomial of degree 2''', or simply a '''quadratic''', is a [[polynomial function]] with one or more variables in which the highest-degree term is of the second degree (i.e. a [[Square (algebra)|square]]).

[[Image:Polynomialdeg2.svg|thumb|right|A quadratic polynomial with two [[real number|real]] [[root of a polynomial|roots]] (crossings of the ''x'' axis) and hence no [[complex number|complex]] roots. Some other quadratic polynomials have their [[minimum]] above the ''x'' axis, in which case there are no real roots and two complex roots.]]

Line 8:

:<math>f(x)=ax^2+bx+c,\quad a \ne 0</math>

in the single variable ''x''. The [[graph of a function|graph]] of a univariate quadratic function is a sharp curve called a [[parabola]], whose axis of symmetry is parallel to the {{math|''y''}}-axis, as shown at right.

If the quadratic function is set equal to zero, then the result is a [[quadratic equation]]. The solutions to the univariate equation are called the [[root of a function|root]]s of the univariate function.