Polynomial functions are among the simplest, most important, and most commonly used mathematical functions. These functions consist of one or more terms of variables with whole number exponents. (Whole numbers are positive integers and zero.) All such functions in one variable (usually x) can be written in this type of format:
In fact, polynomial functions are not too dissimilar to our whole number system. We count with and use a base 10 (decimal) system. Polynomials such as the function above are a "base x" system.
The graphs of polynomial functions have predictable shapes based upon degree and the roots and signs of their first and second derivatives. Higher level derivatives do impart behavioral information into the graphs of fourth degree or higher polynomials, but these effects are usually too subtle to notice, so would seem to have very limited usefulness. Classifying the various shapes, therefore, is thus limited, here, to the information gleaned from the first and second derivatives.
Click on a desired type of polynomial function below in order to view examples and read about particular features.
| Degree Zero (Constant) | Degree Three (Cubic) |
| Degree One (Linear) | Degree Four (Quartic) |
| Degree Two (Quadratic) | Degree Five (Quintic) |
