Editing Quadric (section)

{{short description|Locus of the zeros of a polynomial of degree two}}
{{distinguish|Quadratic (disambiguation){{!}}Quadratic|Quartic (disambiguation){{!}}Quartic}}
{{for-multi|the computing company|Quadrics (company)|quadrics in algebraic geometry|Quadric (algebraic geometry)}}

In mathematics, a '''quadric''' or '''quadric surface''' is a [[generalization]] of [[conic section]]s ([[ellipse]]s, [[parabola]]s, and [[hyperbola]]s). In [[three-dimensional space]], quadrics include [[ellipsoid]]s, [[paraboloid]]s, and [[hyperboloid]]s. 

More generally, a quadric [[hypersurface]] (of dimension ''D'') embedded in a [[higher dimensional]] space (of dimension {{nowrap|''D'' + 1}}) is defined as the [[zero set]] of an [[irreducible polynomial]] of [[degree of a polynomial|degree]] two in {{nowrap|''D'' + 1}} variables; for example, ''D''{{=}}1 is the case of conic sections ([[plane curve]]s). When the defining polynomial is not [[absolutely irreducible]], the zero set is generally not considered a quadric, although it is often called a ''degenerate quadric'' or a ''reducible quadric''.

A quadric is an [[affine algebraic variety]], or, if it is reducible, an [[affine algebraic set]]. Quadrics may also be defined in [[projective space]]s; see {{slink||Normal form of projective quadrics}}, below.