Editing Quadratic function (section)

==Forms of a univariate quadratic function==
A univariate quadratic function can be expressed in three formats:<ref>{{Cite book |last1=Hughes Hallett |first1=Deborah J. |author-link1=Deborah Hughes Hallett |title=College Algebra |last2=Connally |first2=Eric |author-link2=Eric Connally |last3=McCallum |first3=William George |author-link3=William G. McCallum |publisher=[[Wiley (publisher)|John Wiley & Sons Inc.]] |year=2007 |isbn=9780471271758 |page=205}}</ref>
* <math>f(x) = a x^2 + b x + c</math>  is called the '''standard form''',
* <math>f(x) = a(x - r_1)(x - r_2)</math> is called the '''factored form''', where {{math|''r''<sub>1</sub>}} and {{math|''r''<sub>2</sub>}} are the roots of the quadratic function and the solutions of the corresponding quadratic equation.
* <math>f(x) = a(x - h)^2 + k</math> is called the '''vertex form''', where {{math|''h''}} and {{math|''k''}} are the {{math|''x''}} and {{math|''y''}} coordinates of the vertex, respectively.

The coefficient {{math|''a''}} is the same value in all three forms.  To convert the '''standard form''' to '''factored form''', one needs only the [[quadratic formula]] to determine the two roots {{math|''r''<sub>1</sub>}} and {{math|''r''<sub>2</sub>}}. To convert the '''standard form''' to '''vertex form''', one needs a process called [[completing the square]]. To convert the factored form (or vertex form) to standard form, one needs to multiply, expand and/or distribute the factors.