A quadric surface is the zero set of a quadratic expression in three variables—here, the 3D Cartesian coordinates , , and . There are precisely 17 types of quadrics, but some of them are degenerate and others are imaginary.
The nonparabolic family is given by
where , , and can be , , or .
The parabolic family (which overlaps the nonparabolic family somewhat) is given by
This Demonstration shows the chosen polynomial, identifies its type, and plots the zero set. The checkbox toggles between the nonparabolic and parabolic families. All 17 types are represented.