Third degree polynomials are also known as cubic polynomials. Cubics have these characteristics:

- One to three roots.
- Two or zero extrema.
- One inflection point.
- Point symmetry about the inflection point.
- Range is the set of real numbers.
- Three fundamental shapes.
- Four points or pieces of information are required to define a cubic polynomial function.
- Roots are solvable by radicals. (Very advanced and complicated.)

Examining the possible real roots of the first and second derivatives (derivatives are calculus concepts) leads to the three distinct shapes.

Number of Roots |
||

Click for example | ||

2 |
1 |
Graph 1 |

1 |
1 |
Graph 2 |

0 |
1 |
Graph 3 |

Click on any of the images below for specific examples of the three fundamental cubic shapes.