Section 2.3 - Polynomial Functions of Higher Degree with Modeling

Essential Question(s): 

What are the characteristics of higher degree polynomial functions and their graphs?

---

---

Follow these three steps to complete this "flip" lesson.

STEP 1: Preparation 
Title your spiral with the heading above and copy the essential question(s).

STEP 2: Vocabulary & Examples 
Copy and define the following of vocabulary. This can be any tables, properties, theorems, terms, phrases or postulates listed. Review the following examples and copy what is necessary for you. Use the guiding questions for your cornell notes.

Graphs of Polynomial Functions

• When are functions considered a higher degree? (pg 200)
• Review the vocabulary of polynomials. (pg 200)
• How do you graph transformations of monomial functions? (Ex 1 pg 200)
• How do you graph combinations of monomial functions? (Ex 2 pg 201)
• What do polynomials look like in general? (top paragraph on pg 202
• What is the Local Extrema and Zeros of Polynomial Functions Theorem? (pg 202 - read paragraph above theorem)

End Behavior of Polynomial Functions

• Technology note about cubics (pg 203)
• Leading term test for Polynomial End Behavior (pg 204)
• How do you compare the graphs of a polynomials and its leading term? (Ex 3 pg 203)
• How do you apply polynomial theory? (Ex 4 pg 204)

Zeros of Polynomial Functions

• Review what finding real-number zeros are called. (top of pg 205)
• Review finding the zeros of a polynomial function. (Ex 5 pg 205)
• What is multiplicity of a zero of a polynomial function? (read bottom half of pg 205)
• How are zeros affected by odd and even multiplicity? (pg 206)
• How do you sketch the graph of a factored polynomial? (Ex 6 pg 206)

Intermediate Value Theorem

• What is the Intermediate Value Theorem? (pg 206)
• How do you use the Intermediate Value Theorem? (Ex 7 pg 206)
• Review zooming to uncover hidden behavior. (Ex 8 pg 207)

Modeling

• Designing a Box (Ex 9 pg 207)
• What is polynomial interpolation? ( pg 208 whole pg)

STEP 3: Reading
Read the following page(s) and take any extra notes as needed.

• Read pages 200-208.
• Make sure to read the paragraphs between the examples.