Quadratic function: Difference between revisions

Revision as of 15:57, 28 October 2022

Revision as of 16:19, 28 October 2022

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in the single variable ''x''. The [[graph of a function|graph]] of a univariate quadratic function is a [[parabola]], a [[curve]] that has an [[axis of symmetry]] parallel to the {{math|''y''}}-axis.

If thea quadratic function is set[[equation|equated]] equal towith zero, then the result is a [[quadratic equation]]. The solutions toof thea univariatequadratic equation are called the [[rootzero of a function|rootzero]]s of the univariatecorresponding quadratic function.

The bivariate case in terms of variables ''x'' and ''y'' has the form

:<math> f(x,y) = a x^2 + by^2bx y+ cxcy^2 y+ d x+ ey + f \,\!</math>

with at least one of ''a, b, c'' not equal to zero,. andThe anzeros equation settingof this quadratic function equalis, toin zerogeneral gives(that riseis, if a certain expression of the coefficients is not equal to zero), a [[conic section]] (a [[circle]] or other [[ellipse]], a [[parabola]], or a [[hyperbola]]).

:<math> f(x,y) = a x^2 + by^2 + cx y+ d x+ ey + f \,\!</math>

with at least one of ''a, b, c'' not equal to zero, and an equation setting this function equal to zero gives rise to a [[conic section]] (a [[circle]] or other [[ellipse]], a [[parabola]], or a [[hyperbola]]).

A quadratic function in three variables ''x'', ''y,'' and ''z'' contains exclusively terms ''x''², ''y''², ''z''², ''xy'', ''xz'', ''yz'', ''x'', ''y'', ''z'', and a constant: