1. 2.2(a) Notes: Polynomial Functions of Higher Degree
Date:
2.2(a) Notes: Polynomial Functions of Higher Degree
Lesson Objective: Use the LCT to determine end behavior of polynomials, find zeros of polynomials
You will need: calculator, colored pens
Real-World App: What is the maximum volume you can make from a 24” square piece of board?

2. Lesson 1: The Basics of Polynomial Functions

3. Lesson 1: The Basics of Polynomial Functions
Some examples of polynomial graphs and NOT:

4. Lesson 1: The Basics of Polynomial Functions
Some examples of polynomial graphs and NOT:

5. Lesson 1: The Basics of Polynomial Functions
Some examples of parent polynomial graphs:

6. Lesson 2: The Leading Coefficient Test (LCT)
LCT: As x moves without bound to the left or right, the graph of the polynomial eventually rises or falls.
The LCT is used to determine the left-hand and right-hand behavior (the end behavior) of a polynomial.

7. Lesson 2: The Leading Coefficient Test (LCT)
1. When n is odd:
an > an < 0
Falls left, rises right Rises left, falls right

8. Lesson 2: The Leading Coefficient Test (LCT)
2. When n is even:
an > an < 0
Rises left, rises right Falls left, falls right

9. Lesson 2: The Leading Coefficient Test (LCT)
Describe the left-hand and right-hand behavior of the graph of each function.
f(x) = 2x³ – 8x
f(x) = -2x⁴ + 2x²
f(x) = -3.6x⁵ + 5x³ – 1
f(x) = 3x⁴ – 4x³

10. Lesson 3: Zeros – It’s All in a Name

11. Lesson 3: Zeros – It’s All in a Name
# of Zeros: A polynomial has at most n real zeros.

12. Lesson 3: Zeros – It’s All in a Name
# of Zeros: A polynomial has at most n real zeros.
Ways of Finding Zeros:

13. Lesson 3: Zeros – It’s All in a Name
# of Zeros: A polynomial has at most n real zeros.
Ways of Finding Zeros:

14. Lesson 3: Zeros – It’s All in a Name
Find all the real zeros of f(x) = 2x³ – 8x.

15. 2.2(a): DIGI Yes or No
Describe the left-hand and right-hand behavior of the graph of each function.
Find all the real zeros of f(x) = - 2x⁴ + 2x².