1. Unit 5: Polynomial Function Lesson 5.1: Exploring Cubic Functions
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2. Do Now

3. ACT Practice Questions

4. Mastery is evidenced by scoring a 3 out of 4 on the Exit Slip
Objectives
Represent cubic functions using words, tables, equations and graphs.
Interpret the key characteristics of the graph of cubic functions
Analyze cubic functions in terms of their mathematical context and problem context
Build cubic functions from linear and quadratic functions
Mastery is evidenced by scoring a 3 out of 4 on the Exit Slip

5. Common Core Standards A.SSE.1: Seeing Structure in Expressions
A.APR.1 Arithmetic with Polynomials and Rational Expressions
F.IF.7: Interpreting Functions

6. What is a Cubic Function?

7. Cubic Parent Function
What is the parent function of a cubic function?

8. Real Roots of Cubic Function
Relative maximum: highest point in a particular section of a graph.
Relative minimum: lowest point in a particular section of a graph.

9. Roots of Cubic Function
How many x-intercepts does the function have ? How many zeros? Explain your reasoning.
The function has only one x-intercept, (-2, 0) since it crosses the x-axis only once.
The function has three zeros. The zero x = -2 is a multiple root, occurring 3 times.

10. Multiplicity
Multiplicity is how many times a particular number is zero for a given polynomial function.
The Fundamental Theorem of Algebra tells us that a cubic function must have 3 zeros. Roots may be any number including complex ones, and can even appear multiple times.

11. Transformation of Cubic Function

13. Cubic Function in Real World
To find the volume of a cube use
Linear . Linear . linear
Volume is the amount of space that a substance or object occupies
Remember, volume is 3D measure!

14. Quadratic . Linear = cubic

15. Determining the Product of Linear Factors

16. Determining the Product of Quadratic an Linear Factors