Pc 2.2 a_notes

1

2.2 Polynomial Functions of Higher DegreeEssential Question:What is the leading coefficient test?

2

Graphs of Polynomial FunctionsCharacteristics of a polynomial graph:

- __________ (no breaks, holes, or gaps)

- __________ (no sharp edges)

3

What's a Power Function?

Even Odd

4

Whiteboards!

5

Transformations!Ex. 1) Graph.

6

Leading Coefficient TestAs x moves without bound __________ or __________, the graph of the polynomial function eventually ___________ or __________ in the following manner:

n is _____:

7

n is ______:

What does this mean?

8

Rally Coach:

Describe the left and right hand behavior of the function.

9

Zeros of a Polynomial Function

Number of real zeros:

Number of turning points:

Given f is a function of degree n:

10

Real Zeros of Polynomial FunctionsIf f is a polynomial function and a is a real number, the following statements are equivalent:

1) ________ is a _________ of the function f.2) ________ is a _________ of the polynomial equation f(x) = 0.3) ________ is a _________ of f(x).4) ________ is an _____________ of the graph of f.

11

*** Add this below the Real Zeros Slide!

Repeated ZerosA factor (x-a)k yields a repeated zero x = a of ___________ k.

1) If k is ______, the graph _________ x-axis at x = a.

2) If k is ______, the graph _________ the x-axis at x = a

12

Ex. 2) Find all real zeros of Determine the number of turning points as well.

13

Ex. 3﴿ Find a 5th degree polynomial with x=­3, 1, 5, and 6 as zeros.

Bonus Example!!

14

Assignment:

2.2A p. 148 #13-21 (odd), 27-41 (odd)