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{{mergeQuadratic polynomialdate=October 2011}} 

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[[Image:Polynomialdeg2.svgthumbright<center><math>x^2  x  2\!</math></center>]] 

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A '''quadratic function''', in [[mathematics]], is a [[polynomial function]] of the form 





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

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The [[graph of a functiongraph]] of a quadratic function is a [[parabola]] whose axis of symmetry is parallel to the ''y''axis. 

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The expression <math>ax^2+bx+c</math> in the definition of a quadratic function is a '''polynomial of [[Degree of a polynomialdegree]] 2''' or second order, or a '''2nd degree polynomial''', because the highest exponent of ''x'' is 2. 

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

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==Origin of word== 

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The adjective ''quadratic'' comes from the [[Latin]] word ''[[wikt:en:quadratum#Latinquadrātum]]'' (“[[square (geometry)square]]”). A term like ''x''<sup>2</sup> is called a [[square (algebra)square]] in algebra because it is the area of a ''square'' with side ''x''. 

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In general, a prefix [[quadr(i)]] indicates the number [[4 (number)4]]. Examples are quadrilateral and quadrant. ''Quadratum'' is the Latin word for square because a square has four sides. 

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==Roots== 

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{{Further[[Quadratic equation]]}} 

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The [[root of a functionroots]] (zeros) of the quadratic function 

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

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are the values of ''x'' for which ''f''(''x'') = 0. 

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When the [[coefficient]]s ''a'', ''b'', and ''c'', are [[real numbersreal]] or [[complex numberscomplex]], the roots are 

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:<math>x=\frac{b \pm \sqrt{\Delta}}{2 a}, </math> 

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where the [[discriminant]] is defined as 

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:<math>\Delta = b^2  4 a c \, . </math> 






==Forms of a quadratic function== 

==Forms of a quadratic function== 