Quadratic function: Difference between revisions

Revision as of 00:44, 20 June 2025

Latest revision as of 07:19, 20 July 2025

(One intermediate revision by one other user not shown)

Line 1:

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

{{not to be confused with|Quartic function}}

In [[mathematics]], a '''quadratic function''' of a single [[variable (mathematics)|variable]] is a [[function (mathematics)|function]] of the form<ref name="wolfram">{{cite web |last=Weisstein |first=Eric Wolfgang |title=Quadratic Equation |url=https://mathworld.wolfram.com/QuadraticEquation.html |access-date=2013-01-06 |website=[[MathWorld]]}}</ref>

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

Line 81 ⟶ 82:

\end{align}</math>

so the vertex, {{math|(''h'', ''k'')}}, of the parabola in standard form is

: <math> \left(-\frac{b}{2a}, c - \frac{b^2}{4a}\right). </math><ref>{{Citationcite neededbook|datetitle=OctoberCo-ordinate 2022Geometry|first=Percy|last=Coleman|publisher=Oxford University Press|year=1914|page=[https://books.google.com/books?id=TJU5AQAAMAAJ&pg=PA137 137]}}</ref>

If the quadratic function is in factored form

:<math>f(x) = a(x - r_1)(x - r_2)</math>