Content deleted Content added
Citation bot (talk | contribs) Add: publisher, date. | Use this bot. Report bugs. | Suggested by Dominic3203 | Linked from User:Jim.belk/Most_viewed_math_articles_(2010) | #UCB_webform_linked 756/998 |
Link suggestions feature: 3 links added. |
||
Line 24:
When using the term "quadratic polynomial", authors sometimes mean "having degree exactly 2", and sometimes "having degree at most 2". If the degree is less than 2, this may be called a "[[Degeneracy (mathematics)|degenerate case]]". Usually the context will establish which of the two is meant.
Sometimes the word "order" is used with the meaning of "degree", e.g. a second-order polynomial. However, where the "[[degree of a polynomial]]" refers to the ''largest'' degree of a non-zero term of the polynomial, more typically "order" refers to the ''lowest'' degree of a non-zero term of a [[power series]].
===Variables===
A quadratic polynomial may involve a single [[Variable (mathematics)|variable]] ''x'' (the [[univariate]] case), or multiple variables such as ''x'', ''y'', and ''z'' (the multivariate case).
====The one-variable case====
Line 187:
A '''bivariate quadratic function''' is a second-degree polynomial of the form
:<math> f(x,y) = A x^2 + B y^2 + C x + D y + E x y + F,</math>
where ''A, B, C, D'', and ''E'' are fixed [[coefficient]]s and ''F'' is the [[constant term]].
Such a function describes a quadratic [[Surface (mathematics)|surface]]. Setting <math>f(x,y)</math> equal to zero describes the intersection of the surface with the plane <math>z=0,</math> which is a [[locus (mathematics)|locus]] of points equivalent to a [[conic section]].
| |||