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While a surface may commonly be called "quadric", "quadratic" is overwhelmingly the usual term for a function. |
golden ratio is important; also fixed references |
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[[Image:Polynomialdeg2.svg|thumb|right|A quadratic polynomial with two [[real number|real]] [[root of a polynomial|roots]] (crossings of the ''x'' axis) and hence no [[complex number|complex]] roots. Some other quadratic polynomials have their [[minimum]] above the ''x'' axis, in which case there are no real roots and two complex roots.]]
For example, a [[univariate]] (single-variable) quadratic function has the form<ref name="wolfram">{{cite web |last=Weisstein |first=Eric Wolfgang |title=Quadratic Equation |url=
:<math>f(x)=ax^2+bx+c,\quad a \ne 0,</math>
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==Forms of a univariate quadratic function==
A univariate quadratic function can be expressed in three formats:<ref>{{Cite book |last=Hughes Hallett |first=Deborah J. |author-link=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''',
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===Upper bound on the magnitude of the roots===
The [[absolute value|modulus]] of the roots of a quadratic <math>ax^2+bx+c</math> can be no greater than <math>\frac{\max(|a|, |b|, |c|)}{|a|}\times \phi, </math> where <math>\phi</math> is the [[golden ratio]] <math>\frac{1+\sqrt{5}}{2}.</math><ref>{{Cite journal |last=Lord
==The square root of a univariate quadratic function==
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==References==
{{Reflist}}
*{{Cite book |last=Glencoe |first=McGraw-Hill |title=Algebra 1 |isbn=9780078250835}}
*{{Cite book |last=Saxon |first=John H. |title=Algebra 2 |isbn=9780939798629}}
==External links==
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