1. Polynomial Functions 33 22 11 Definitions Degrees Graphing

2. Definitions  Polynomial  Monomial  Sum of monomials  Terms  Monomials that make up the polynomial  Like Terms are terms that can be combined 2

3. Degree of Polynomials  Simplify the polynomial  Write the terms in descending order  The largest power is the degree of the polynomial 3

4. 4 A LEADING COEFFICIENT is the coefficient of the term with the highest degree. (must be in order) What is the degree and leading coefficient of 3x 5 – 3x + 2 ? Degree of Polynomials

5. 5 Polynomial functions with a degree of 1 are called LINEAR POLYNOMIAL FUNCTIONS Polynomial functions with a degree of 2 are called QUADRATIC POLYNOMIAL FUNCTIONS Polynomial functions with a degree of 3 are called CUBIC POLYNOMIAL FUNCTIONS

6. 6 Cubic Term Terms of a Polynomial Quadratic Term Linear Term Constant Term

7. End Behavior Types  Up and Up  Down and Down  Down and Up  Up and Down  These are “read” left to right  Determined by the leading coefficient & its degree 7

8. Up and Up

9. Down and Down

10. Down and Up

11. Up and Down

12. Determining End Behavior Types n is evenn is odd a is positive a is negative 12

13. END BEHAVIOR Degree: Even Leading Coefficient: + f(x) = x 2 End Behavior: Up and Up

14. END BEHAVIOR Degree: Even Leading Coefficient: – End Behavior: f(x) = -x 2 Down and Down

15. END BEHAVIOR Degree: Odd Leading Coefficient: + End Behavior: f(x) = x 3 Down and Up

16. END BEHAVIOR Degree: Odd Leading Coefficient: – End Behavior: f(x) = -x 3 Up and Down

17. Turning Points  Number of times the graph “changes direction”  Degree of polynomial-1  This is the most number of turning points possible  Can have fewer 17

18. Turning Points (0) f(x) = x + 2 Linear Function Degree = 1 1-1=0

19. Turning Points (1) f(x) = x 2 + 3x + 2 Quadratic Function Degree = 2 2-1=1

20. Turning Points (0 or 2) f(x) = x 3 + 4x 2 + 2 Cubic Functions Degree = 33-1=2 f(x) = x 3

21. Graphing From a Function  Create a table of values  More is better  Use 0 and at least 2 points to either side  Plot the points  Sketch the graph  No sharp “points” on the curves 21

22. Finding the Degree From a Table  List the points in order  Smallest to largest (based on x-values)  Find the difference between y-values  Repeat until all differences are the same  Count the number of iterations (times you did this)  Degree will be the same as the number of iterations 22

23. Finding the Degree From a Table xy -3 -2-7 -3 05 111 29 3-7 23 -6 4 8 6 -2 -16 10 4 -2 -8 -14 -6