Content deleted Content added
Srich32977 (talk | contribs) Cleaned up using AutoEd |
Citation bot (talk | contribs) Add: jstor, doi, author-link1, authors 1-1. Removed parameters. Some additions/deletions were parameter name changes. | Use this bot. Report bugs. | Suggested by Neko-chan | #UCB_webform 45/500 |
||
Line 47:
==Forms of a univariate quadratic function==
A univariate quadratic function can be expressed in three formats:<ref>{{Cite book |
* <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.
Line 133:
===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 |first=Nick |date=2007-11-01 |title=Golden Bounds for the Roots of Quadratic Equations |url=https://doi.org/10.2307/40378441 |journal=[[The Mathematical Gazette]] |volume=91 |issue=522 |pages=549 |doi=10.1017/S0025557200182324 |jstor=40378441 }}</ref>
==The square root of a univariate quadratic function==
| |||