Objective

To classify polynomials
To graph polynomial functions and describe end behavior.

Definitions

• Monomial: a real number, a variable, or a product of real numbers and variables with whole number exponents

• Polynomial: a monomial or a sum or difference of monomials

• Polynomials have no variables in denominators or exponents, no roots or absolute values of variables, and all variables have whole number exponents.

Classifying Polynomials

• The degree of a polynomial is the degree of the term with the greatest degree (highest exponent)

• The leading coefficient is the coefficient of the first term

A polynomial is written in standard form when:

• The terms are written in descending order by degree

• All like terms have been combined

A polynomial can be clasified by its number of terms

A polynomial with two terms is called a binomial. A polynomial with three terms is called a trinomial.

The degree of a polynomial function affects the shape of the graph and determines the number of turning points (the point or points where a graph changes direction).

If a turning point is higher than any nearby point, its called a relative maximum.

If a turning point is lower than any nearby point, its called a relative minimum.

The maximum and minimum values are called extrema.

The turning points define where a function is increasing or decreasing.

End behavior

End behavior

End behavior

Good work!

Please complete the last section of the notes handout.