Section 2-3: Graphing Polynomial Functions

1. Section 2-3: Graphing Polynomial Functions Pre-Calculus Day 1

2. Objectives • Determine what are polynomial function. • Understand End Behavior and how to predict it. • Sketch graph of factored function. • Sketch graph of non-factored polynomial. • Write the equation of a polynomial given its graph. • Sketching and find the features of a polynomial that does not factor.

3. Warm-Up • We will be working in groups today … • In order to find your group, you will be given a flashcard with a piece of information on it. Group yourself with classmates that have THE SAME piece of information. • Your group should have members. • Once you find everyone, move desks together so you are all facing each other.

4. Determine A Polynomial Function • From p.4: • All the coefficients are real numbers • Exponents are real numbers • is the leading coefficient • n is the degree of the polynomial • is the constant term

5. Apply It! • You will have 3 minutes to complete 1-4 on page 5 of your workbook. • Guidelines for Success • Work individually • Ask questions if you are confused. • Be prepared to support your final answers.

6. Objectives • Determine what are polynomial function. • Understand End Behavior and how to predict it. • Sketch graph of factored function. • Sketch graph of non-factored polynomial. • Write the equation of a polynomial given its graph. • Sketching and find the features of a polynomial that does not factor.

7. Discovery • Lets figure out what is going on with End Behavior. • You will have 5 minutes to discuss and explain the problems provided below. • Guidelines for Success • Work in pairs.   • Ask questions if you are confused. • Be prepared to support your final answers. What is the sign of your answer when you plug into ? Why? What is the sign of your answer when you plug into ? Why? Why does equal a positive answer? Why does equal a negative answer?

8. End Behavior • Lets figure out what is going on with End Behavior.

9. Apply It! • You will have 4 minutes to complete 4a-d on page 5 of your workbook. • Guidelines for Success • Work individually. • Ask questions if you are confused. • Be prepared to support your final answers.

10. So you think you got it huh? Challenge: Write an equation for a graph that has two turns and disjoint end behavior.

11. Homework • Source: Workbook 1 • Complete Ex. 4 #1-4 on page 5. • Complete #5-8 on page 6.

12. Objectives • Determine what are polynomial function. • Understand End Behavior and how to predict it. • Sketch graph of factored function. • Sketch graph of non-factored polynomial. • Write the equation of a polynomial given its graph. • Sketching and find the features of a polynomial that does not factor.

13. Sketch the Graph of a Factored Polynomial • Sketch the graph of • Find and plot zeros • Perform sign analysis • Sketch graph

14. Sketch the Graph of a Factored Polynomial • You will have 10minutes to discuss and explain the problems provided below. • Guidelines for Success • Work in threes.    • Ask questions if you are confused. • Be prepared to support your final answers. • You practice: Challenge: What is the connection between these two?

15. Objectives • Determine what are polynomial function. • Understand End Behavior and how to predict it. • Sketch graph of factored function. • Sketch graph of non-factored polynomial. • Write the equation of a polynomial given its graph. • Sketching and find the features of a polynomial that does not factor.

16. Write the equation, given the graph • Quadratic • Plug in a and b as roots • Use an additional pointto plug in for x and y • Solve for k • Plug in a, b, and k

17. Write the equation, given the graph • Cubic • Plug in a, b, and c as roots • Use an additional pointto plug in for x and y • Solve for k • Plug in a, b, c, and k

18. You try! • Find the equation: (0, 12)

19. Round Table Practice Sess • Source: Textbook • Page: 66 • Problems: #1-9, #13, #15

20. Homework Round 2 • In your textbook complete #6-16 (evens) on pg. 66

21. Objectives • Determine what are polynomial function. • Understand End Behavior and how to predict it. • Sketch graph of factored function. • Sketch graph of non-factored polynomial. • Write the equation of a polynomial given its graph. • Sketching and find the features of a polynomial that does not factor.

22. Sketch the graph of a non-factored polynomial • Same process as before, but now we must first factor. • You try!

23. Objectives • Determine what are polynomial function. • Understand End Behavior and how to predict it. • Sketch graph of factored function. • Sketch graph of non-factored polynomial. • Write the equation of a polynomial given its graph. • Sketching and find the features of a polynomial that does not factor.

24. The Unfactorable So Now What … Calculator Steps Y= Enter your function. Graph 2nd then Trace Select either: 2: Zero 3: Minimum 4: Maximum • Your nutty pre-calc teacher wants you to graph a polynomial function that cannot factor. • TI-84 TO THE RESCUE • Sure is a good thing you purchased all of your class supplies like a champ.

25. Practice Sess • Page: 6-7 • Problems: #5-16 • Additional Notes: For #9-16 do not just graph. Please also find the zeros, local max and local minif applicable!!!

26. Homework • Source: Workbook • Page: 6-7 • Problems: #9-16 • Additional Notes: For #9-16 do not just graph. Please also find the zeros, local max and local minif applicable!!!