Pre-AP Pre-Calculus Chapter 2, Section 3

1. Pre-AP Pre-CalculusChapter 2, Section 3 Polynomial Functions of Higher Degree with Modeling 2013 - 2014

2. Polynomial Functions of Higher Degrees & Vocabulary • Cubic Functions – • Quartic Functions – • Term – • Coefficient – • Leading term –

3. Graphical Transformations of Monomial Functions • Describe how the monomial was transferred into the given equation.

4. Graph the polynomial function, locate its extrema and zeros.

5. Graph the polynomial function, locate its extrema and zeros.

6. Cubic Functions: 2 with positive leading coefficients, 2 with negative leading coefficients

7. Quartic Functions: 2 with positive leading coefficients, 2 with negative leading coefficients

8. Theorem: Local Extrema and Zeros of Polynomial Functions • A polynomial function of degree n has at most n – 1 local extrema and at most n zeros.

9. End Behavior Exploration • On the following slides, graph each equation one at a time. • Use the window [-5, 5] by [-15, 15]. • Describe the end behavior using and

13. Comparing Graphs • Sketch the graph showing both functions • Zoom out till the graphs look nearly identical. • Note the final window

14. Applying Polynomial Theory • Graph the polynomial in a window showing its extrema, zeros, and end behavior. • Describe the end behavior using limits.

15. Applying Polynomial Theory • Graph the polynomial in a window showing its extrema, zeros, and end behavior. • Describe the end behavior using limits. • g

16. Find the zeros of the function(algebraically)

17. Factors & Multiplicity • When a factor is repeated, as in , you can say the polynomial has a repeated zero. • The given function has two repeated zeros: x = _____ and x = ______. • Because the factor (x – 2) occurs three times, the multiplicity of the zero of the function is 3. (it occurs 3 times) • Because the factor (x + 1) occurs twice, the multiplicity of the zero of the function is 2. (it occurs twice)

18. Use the Zoom!! • Find all real zeros of

19. Dixie Packaging Company has contracted to make boxes with a volume of approximately 484 in3 . Squares are to be cut from the corners of a 20-in. by 25-in. piece of cardboard, and the flaps folded up to make an open box. What size squares should be cut from the corners?

20. Factor the given equation

21. Before you leave class • Section 2.3 exercise, # 63

22. Ch. 2.3 Homework • Pg. 209 - 212: #’s 3, 9, 15, 17, 23, 25, 29, 37, 41 (ignore directions about stating whether it crosses the x-axis at corresponding x-axis), 53, 67, 73 • (12 total problems) • Gray Book: pages 193 - 195