1. Polynomial Functions of Higher Degree
Section 2.2
Polynomial Functions of Higher Degree

2. Objective By following instructions students will be able to:
Use transformations to sketch graphs of polynomial functions.
Use the Leading Coefficient Test to determine the end behavior of graphs of polynomial functions.
Find and use zeros of polynomial functions to sketch their graphs.

3. Recall

4. Polynomial Functions
Polynomial Functions are continuous – no breaks, holes, sharp turns or gaps.

5. Non Polynomial Functions
Polynomial Functions are continuous – no breaks, holes, sharp turns or gaps.

6. Example 1:
Sketch the graph of each polynomial function. a) b) c)

7. Leading Coefficient Test
Leading Coefficient is Positive
Leading Coefficient is Negative
Degree is EVEN
(BOWL)
Degree is ODD
(SNAKE)

8. Example 2:
Sketch the graph of each polynomial function. a) b) c)

9. U-TRY #1
Sketch the graph of: a) b) c) d) e)

10. Real Zeros of Polynomial Functions
If f is a polynomial function and a is a real #, the following statements are equivalent.
1. x=a is a zero of the function f.
2. x=a is a solution of the polynomial f(x)=0.
3. (x-a) is a factor of the polynomial f(x).
4. (a,0) is an x-intercept of the graph of f.
Relative Extrema
Points in between the roots.
Multiplicity
A repeated solution.

11. Example 3:
Find all real zeros of

12. Example 4:
Find all real zeros and relative extrema of

13. Example 5:
Find all real zeros of

14. U-TRY #2 Find all real zeros of: a) b)
Graph and approximate any relative extrema. d) e)

15. Example 6:
Find polynomial functions with the following zeros. a) b) c)

16. Example 7:
Sketch the graph of by hand.

17. Example 8:
Sketch the graph of by hand.

18. U-TRY #3
Find a polynomial function that has the given zeros. a) b)

19. Revisit Objective Did we…
Use transformations to sketch graphs of polynomial functions?
Use the Leading Coefficient Test to determine the end behavior of graphs of polynomial functions?
Find and use zeros of polynomial functions to sketch their graphs?

20. Homework HW: I: pg 132 #s 33 pg 144 #s 40, 69
II: pg 156 #1-9, 13, 14, ODD, 49, 53, 57, 61, 65, 68, 71, 77
III:pg159 #s