Cubic function - Definition and Overview

Polynomial of degree 3

A cubic function is a function of the form

<math>f(x)=ax^3+bx^2+cx+d<math>,

where a is nonzero; or in other words, a polynomial with a degree of three. The derivative of a cubic function is a quadratic function.

Bipartite cubics

The graph of

<math>y^2 = x(x-a)(x-b)<math>

where <math>0 < a < b<math> is called a bipartite cubic. This is from the theory of elliptic curves.

You can graph a bipartite cubic on a graphing device by graphing the function

<math>f(x) = \sqrt{x(x-a)(x-b)}<math>

corresponding to the upper half of the bipartite cubic. It is defined on

<math>(0,a) \cup (b,+\infty)<math>.

Example Usage of function