1. 2.3 Graphing Polynomial Functions Objective: I will be able to graph polynomial functions and describe the end behavior.

5. Quartic functions are similar to quadratic functions in that they have somewhat of a “U” shape

6. Parent Graphs f(x)=x 2 f(x)=x 3 f(x)=x 4 f(x)=x 5 f(x)=x 6 f(x)=x 7

7. Even Degree Functions Even Functions- functions who reflect over the x-axis. End Behavior: What are the ends of these functions doing? What happens if the functions are negative?

8. Odd Degree Functions Odd Functions- functions who rotate around the origin. End Behavior: What are the ends of these functions doing? What happens if they functions are negative?

9. Let’s figure out what’s going on with end behavior Think about the below questions, on your own. Be prepared to support your final answers.

10. Graph these on your calculator and figure out how to know the end behavior just by looking at the equation. Use detailed descriptions! Guidelines for Success Work in pairs. Ask questions if you are confused. Be prepared to support your final answers.

11. Organize Your Data L.C. > 0L.C. < 0 n odd n even

12. End Behavior Aerobics f(x) = x 2 g(x) = -x 4 H(x) = x 3 J(x) = -x 9 m(x) = x 17 B(x) = 2x 12 w(x) = -x 70 V(x) =x 101 f(x) = x 2 + 2x g(x) = -2x 4 + x H(x) = x 3 – x J(x) = -4x 5 + 7x 2 – 2 m(x) = 15x 11 – 4x 7 + 5x – 1 B(x) = ½x 26 + 2 w(x) = -x 77 + 5x 23 + 4 V(x) = 23x 44 – 22x

13. Sketching the Graph of a Polynomial What I expect: The zeros of the polynomial The y-intercept Appropriate end behavior One point between each zero to approximate the shape

14. Sketch a graph: f(x)= (x-3)(x+1)(2x-1)

15. Sketch a graph: f(x)=(x+3)(x+1)(x-1)(x-2)

16. Sketch a graph: f(x) = -x(x+2)(x-1)

17. Exit Ticket Determine the end behavior of: Assignment: Workbook pg. 5 all problems

18. Recall from yesterday What cubic functions look like… Must have 3 zeros! (real or imaginary) Will cross x-axis 3 times (usually) What quartic functions look like… Must have 4 zeros! (real or imaginary) Will cross x-axis 4 times (usually)

19. Sketch a graph: f(x) = x(x+3)(x-4)(-x+1) Zeros: Y-intercept: Degree/Leading coefficient: 1 point between each root:

20. Sketch a graph: f(x) = (x-1)(x-3)(x-4)(x-3) Uh oh! We have 2 of the same root. What happens now? The double root is tangent to the x-axis (the curve “bounces off” the x-axis).

21. Sketch a graph: f(x) = (-x-1)(x-3) 2

24. Y= Enter your function. Graph Plot points from table 2 nd then Trace Select either: 2: Zero 3: Minimum 4: Maximum

25. Domain and Range! Domain: the set of all the values for x in a given function (input values) Range: the set of all the values for y in a given function (output values)

26. Find the domain and range of the following functions (with your partner!)

27. Write the equation, domain, and range given the graph

29. You try! Find the equation, domain, and range: (0, 12)

30. Practice Session! Complete the following on your own or with a partner: Graphing Polynomials Worksheet pg. 67 #29-32

31. Exit Slip! Homework: pg. 6-7 #5-16 On a separate sheet of paper, please respond to the following: -2 new things you learned today -At least 1 question you still have on this topic (if any) -On a scale of 1-10, how comfortable are you with identifying end behavior and graphing polynomials? Draw a bar graph to show your level of confidence.