6 2 Evaluating and Graphing Polynomial Functions ObjectivesAssignment

6. 2 Evaluating and Graphing Polynomial Functions

Objectives/Assignment 1. Evaluate a polynomial function 2. Graph a polynomial function 3. Assignment: 15 -79 odd

A polynomial function is a function of the form: The degree of the polynomial. This is called the lead coefficient. All the exponents are whole numbers. The constant term

Here is a summary of common types of polynomial functions. Degree Type 0 Constant 1 Linear 2 Quadratic 3 Cubic 4 Quartic Standard Form

Recall to evaluate a polynomial you could use direct substitution. For example evaluate: when x = 3. Here is another way to evaluate a polynomial function called synthetic substitution: x-value Mult. By 3 3 2 2 0 -8 ADD 6 18 10 6 f(3)=98 5 -7 30 105 35 98

Use synthetic substitution to evaluate the polynomial at the given value. Check your result by direct substitution.

Here are 4 graphs: Notice for each as: and We call this the “end behavior” of a polynomial function; that is the value (y) of a function as x approached positive infinity and negative infinity.

Here are 4 more graphs: Notice again for each as: and We call this the “end behavior” of a polynomial function; that is the value (y) of a function as x approached positive infinity and negative infinity.

For polynomial functions: The end behavior is determined by the lead coefficient and degree. n even n odd