1. Skill 1: Classifying a Polynomial Function by Equation and Graph Mrs. Castro

3. Polynomials. What are they and why do I have to learn about them? “Polynomials define simple curves in the language of mathematics so that they may be easily analyzed and modified. Simple curves can be combined to closely approximate more complicated curves. Planets, weather, etc. move in curves. Mechanical forces, chemical and biological processes, etc. are not constant but change over space and time. These changes and other changes like fluctuations in the economy can be approximated by curves. Also, televisions, computers, phones, music players, etc. all receive signals that are sine waves (curves). Does an electrical engineer factor polynomials on a daily basis? No. A novelist doesn't analyze the structure of each sentence, but at some point the novelist needed to learn sentence structure to write books. In the same way, polynomials are the building blocks of all these sciences.” 3

4. Celebrity Polynomials The Legendre Polynomial… in electrostatics. 4

5. Celebrity Polynomials The Gegenbauer Polynomial… in harmonic analysis. 5

6. Celebrity Polynomials The Chebyshev Polynomials… in approximation theory. 6

7. Identifying Polynomials Polynomials have: 1. NO variables or exponents in denominators, 2. NO roots or absolute values of variables, and 3.All variables have whole number exponents. Terms are separated by “+” and “-”. 7

8. With Your Whiteboard… Use a simple “Y” or “N” to indicate your response to the questions. 8

9. Identifying Polynomials Is this a polynomial? 9

10. Identifying Polynomials Is this a polynomial? 10

11. Identifying Polynomials Is this a polynomial? 11

12. Identifying Polynomials Is this a polynomial? 12

13. Identifying the Degree of a Polynomial The degree of a polynomial is the highest exponent. 13

14. Identifying the Degree of a Polynomial 14

15. You Try: Identifying the Degree of a Polynomial 15

16. Identifying the Number of Terms in a Polynomial STANDARD FORM: All “like” terms are combined and the polynomial’s terms are ordered from highest exponent to the lowest exponent. The number of terms of a polynomial can be found by 1) combining like terms and then 2) counting each term. MonomialBinomialTrinomialPolynomial w/ ____ terms

17. Identifying the Number of Terms in a Polynomial

19. Classifying Polynomial Function by Equation

20. Classifying Polynomial Functions by Equation

21. You Try: Classifying Polynomial Functions by Equation

22. Sketching/Identifying the Shape of a Polynomial Function

23. You Try: On your whiteboard, indicate the degree of the function.

24. You Try: From memory, sketch a polynomial function that has a degree of 4. Sketch a polynomial function that has a degree of 3. Sketch a polynomial function that has a degree of 10.

25. Evaluating Polynomial Functions for a Given Input

27. Exit Quiz: