View source for Quadratic function

[[File:Graph of quadratic function y=x²-3x-4.png|alt=A quadratic graph that has two real answers.|thumb|A quadratic graph with two [[Real number|real]] answers and no [[Complex number|complex]] answers. Other quadratic graph have no real answers and 2 complex answers.]]
In [[elementary algebra]], a '''quadratic function''' is a [[function (mathematics)|function]] containing a '''quadratic expression''', a [[polynomial]] where the [[Degree (mathematics)|degree]] (the highest [[exponent]] it has) is [[2 (number)|2]]. The single-variable standard form of a quadratic function isː
<math display=block>f(x)=ax^2+bx+c</math>
where <math>a</math>, <math>b</math> and <math>c</math> are all constants and <math>a\ne 0</math>.

When such a function gets plotted on a [[graph]] where <math>f(x)=y</math>, a [[curve]] that extends [[Infinity|infinitely]] called a [[parabola]] will appear.

When a quadratic function is set to some value, it makes a [[quadratic equation]]. When the value is zero, the equation is said to be in standard form, and its solutions are the places where the function crosses the <math>x</math>-axis.
== Properties ==
Quadratic functions have a single [[extremum]]. This point, which is a minimum if <math>a>0</math> and a maximum if <math>a<0</math>, is called the [[vertex]] of the parabola.

The [[derivative]] of a quadratic function is a [[linear function]].
== Etymology ==
The word ''quadratic'' comes from the [[Latin]] word ''quadrātum'' ("[[square]]"). The highest degree term, <math>x^2</math>, is the [[area]] of a [[square]] with side length <math>x</math>. The word "quadratic" is applied to many things in mathematics that involve this <math>x^{2}</math> term. A similar etymology is shared with [[cubic function]]s, which have an <math>x^{3}</math> term that is the [[volume]] of the [[cube]] of side length <math>x</math>. Higher degrees like [[quartic function]]s and up take their name from the degree directly using [[numeric prefix]]es.

{{Polynomials}}

== Quadratic Function Media ==
<gallery widths='160px' heights='100%' mode='traditional' caption=''>
File:Polynomialdeg2.svg|A quadratic polynomial with two [[real number|real]] roots (crossings of the {{mvar|x}} axis).

File:Function ax^2.svg|Function f(x)=ax2{\displaystyle f(x)=ax^{2}}

File:Function x^2+bx.svg|Function f(x)=x2+bx{\displaystyle f(x)=x^{2}+bx}

File:Function x^2-bx.svg|Function f(x)=x2+bx{\displaystyle f(x)=x^{2}+bx}
</gallery>
{{Math-stub}}


[[Category:Algebra]]