1. Polynomial Functions 1
Definitions 2
Degrees 3
Graphing

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

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

4. What is the degree and leading coefficient of 3x5 – 3x + 2 ?
Degree of Polynomials
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 3x5 – 3x + 2 ?

5. Degree of Polynomials
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. Terms of a Polynomial Cubic Term Linear Term Quadratic 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

8. Up and Up

9. Down and Down

10. Down and Up

11. Up and Down

12. Determining End Behavior Types
Leading Term
n is even
n is odd
a is positive
a is negative
Up and Up
Down and Up
Down and Down
Up and Down

13. Leading Coefficient: +
END BEHAVIOR
f(x) = x2
Degree: Even
Leading Coefficient: +
End Behavior:
Up and Up

14. Leading Coefficient: –
END BEHAVIOR
f(x) = -x2
Degree: Even
Leading Coefficient: –
End Behavior:
Down and Down

15. Leading Coefficient: +
END BEHAVIOR
f(x) = x3
Degree: Odd
Leading Coefficient: +
End Behavior:
Down and Up

16. Leading Coefficient: –
END BEHAVIOR
f(x) = -x3
Degree: Odd
Leading Coefficient: –
End Behavior:
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

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

19. Quadratic Function f(x) = x2 + 3x + 2 Degree = 2 2-1=1
Turning Points (1)
Quadratic
Function
f(x) = x2 + 3x + 2
Degree = 2
2-1=1

20. f(x) = x3 + 4x2 + 2 Cubic Functions Degree = 3 3-1=2
Turning Points (0 or 2)
f(x) = x3
f(x) = x3 + 4x2 + 2
Cubic
Functions
Degree = 3
3-1=2

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

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

23. Finding the Degree From a Tablex y -3 -1 -2 -7 5 1 11 2 9 3
1st
2nd
3rd -6 10 -6 4 4 -6 8 -2 -6 6 -8 -6 -2
-14
-16
3rd Degree Polynomial