1. Polynomial Functions and Models Section 5.1

2. Polynomial Functions

3. Is it a polynomial? If so, what is the degree?

4. Example: Factors of a Polynomial

5. Zeros of a Polynomial

6. True or False

7. Exercise 42 – Page 342

8. True or False

9. Multiplicity

10. Determine the real zeros and their multiplicity.

11. 1.List the real zeroes. 2.Determine the multiplicity of each. 3.At each real zero, determine if the graph touches or crosses.

12. The role of multiplicity

13. True or False The degree of the polynomial is even.

14. End Behavior The left side of the graph is down. The right side of the graph is up.

15. End Behavior Describe the end behavior for this graph. The left is ________ and the right is _________.

16. End Behavior Leading coefficient is negative Leading coefficient is positive Degree is odd Left up Right down Left down Right up Degree is even Left down Right down Left up Right up

17. Straight Line (odd degree) Leading coefficient is negativeLeading coefficient is positive

18. Quadratic (even degree) Leading coefficient is negativeLeading coefficient is positive

20. Cubic Modeling Suppose we have a 10 inch by 20 inch piece of metal. A square will be cut out of each corner. The sides will be turned up to create a box. We want to determine the size of the square that should be cut out in order to maximize the volume of the box.

21. Find a formula for the volume of the box.

22. Volume Use the data points to fit a cubic that will model the volume of the box based on the amount that is cut out of each corner. Graph the model and determine the square that should be cut out to maximize the volume.