1. Chapter 5 Polynomials and Polynomial Functions © Tentinger

2. Essential Understanding and Objectives Essential Understanding: A polynomial function has distinguishing behaviors. Objectives Students will be able to: Classify polynomial functions Graph polynomial functions and describe the end behavior

3. Iowa Core Curriculum Algebra A.SSE.1a. Interpret expressions that represent a quantity in terms of its context. ★ Interpret parts of an expression, such as terms, factors, and coefficients. Functions F-IF.4. For a function that models a relationship between two quantities, interpret key features of graphs and tables in terms of the quantities, and sketch graphs showing key features given a verbal description of the relationship. Key features include: intercepts; intervals where the function is increasing, decreasing, positive, or negative; relative maximums and minimums; symmetries; end behavior; and periodicity. ★ F.IF.7 Graph functions expressed symbolically and show key features of the graph, by hand in simple cases and using technology for more complicated cases. ★ F.IF.7c. Graph polynomial functions, identifying zeros when suitable factorizations are available, and showing end behavior.

5. Vocabulary Monomial: A real number, a variable, or product of a real number and one or more variables with whole number exponents Degree of a Monomial: Exponent of the variable Polynomial: Monomial or the sum of monomials Degree of a Polynomial: The largest degree among its monomial terms Standard Form of a Polynomial Function: Arranges the terms by degree in descending numerical order. Constant is always last. (show general equation)

6. Classifying Polynomials: Degrees zero through five have specific name.

7. Write each polynomial in standard form. What is the classification of each polynomial by degree and number of terms? 1. 3x 3 – x + 5x 4 2. 3 – 4x 5 + 2x 2 + 10 3. -3x + 4x 3 + 7x - 3

8. End Behavior The degree of a polynomial function affects the shape of its graph and the max number of turning points. It also determines end behavior. 4 types of end behavior When a is positive, the graph has n – 1 turning points. An odd degree has an even number of turning points and an even degree has an odd number of turning points.

9. Example What is the end behavior of the graph? 1. y = -4x 3 + 2x 2 +7 2. y = 3x 4 – 2x 3 + x – 1

10. Graphing Cubic Equations Make a table of values to graph the middle parts. Then use the end behavior to sketch the rest of the graph. What is the graph of each cubic function/ Describe the graph, including end behavior, turning points, and increase/decreasing intervals. 1. y = -x 3 +2x 2 – x – 2 2. y = x 3 – 1

11. Determining Degrees of Functions

12. What is the degree of the function?

13. Homework Pg. 285-286 #9 – 36 (3s), 38, 39, 47 – 49, 54