Warm-Up

1. Warm-Up • State an equation for the following polynomial:

2. Polynomial Graphing Pt. 2

3. Learning Targets • End Behavior • Turns or “Bumps” for each polynomial • Investigate Roots

4. End Behavior

5. Types of Roots • Polynomial solutions are made up of complex roots • A root is where the polynomial’s graph will intersect with the x-axis • A complex root describes two different types of roots: • Real Roots • Imaginary Roots (we will get to these next week)

6. Root Classifications • We classify the type of Real Root based on the degrees of each term and how it interacts with the x-axis. • Types: • Single Root • Double Root • Triple Root • And so on…

7. Examples: • Single Roots

8. Examples: • Double Roots

9. Examples: • Triple Roots

10. You Try • Classify each type of root:

11. Practice • Sketch the following polynomials, describe the end behavior and classify the roots: • 1) • 2) • 3)

12. #1 This is only a sketch

13. #2 This is only a sketch

14. #3 This is only a sketch

15. Turns In a Graph • What determines the number of turns the graph of a polynomial will have? • End Behavior • Degree of the Leading Term • Degrees of each factor, or the types of roots • The maximum number of turns a polynomial can have is (n-1) where n is the degree of the leading term

16. For Tonight • On the worksheet from Thursday: • Describe the end behavior using the correct math notation • Circle each root on the graph. • Label each root as single, double or Triple.

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