Warm-Up 2/201.

D

Rigor:You will learn how to analyze and graph

equations of polynomial functions.

Relevance:You will be able to use graphs and equations of

polynomial functions to solve real world problems.

2-2 Polynomial Functions

Example 1: Graph each function.

f(x) is similar to and is translated right 2 units.

g(x) is similar to and is reflected in the x-axis and translated up 1 unit.

Example 2: Describe the end behavior.

a. Degree is 4.Leading Coefficient is 3.and

b. Degree is 7.Leading Coefficient is – 2.and

c. Degree is 3.Leading Coefficient is 1.and

Example 3: State the number of possible real zeros and turning points of . Then determine all of the real zeros by factoring.

𝑥3−5 𝑥2+6 𝑥=0

Degree is 3.f has at most 3 distinct real zeros.

f has at most 2 turning points.

𝑥 (𝑥2− 5𝑥+6 )=0𝑥 (𝑥− 2 ) (𝑥− 3 )=0f has real zeros at x = 0, 2, and 3.

Example 4: State the number of possible real zeros and turning points of . Then determine all of the real zeros by factoring.

𝑥4 −3 𝑥2− 4=0

Degree is 4.g has at most 4 distinct real zeros.

g has at most 3 turning points.

(𝑥2 )2 −3 (𝑥2 ) − 4=0

𝑢2 −3𝑢− 4=0

g has real zeros at x = – 2 and 2.

(𝑢+1)(𝑢− 4)=0(𝑥2+1)(𝑥2− 4 )=0

or

𝑥2=−1𝑥=±√−1  

𝑥2=4𝑥=± 2

Let

Example 5: State the number of possible real zeros and turning points of . Then determine all of the real zeros by factoring.

−𝑥4 −𝑥3+2 𝑥2=0

Degree is 4.h has at most 4 distinct real zeros.

h has at most 3 turning points.

−𝑥2 (𝑥2+𝑥− 2 )=0

h has real zeros at x = 0, 1 and –2. The zero at 0 has a multiplicity of 2.

−𝑥2(𝑥−1)(𝑥+2)=0 or or

𝑥=0 𝑥=1 𝑥=−2𝑥=0

Example 6:

𝑥 (2𝑥+3)(𝑥− 1)2=0

a. Degree is 4. f has at most 4 distinct real zeros and at most 3 turning points.

b. f has real zeros at x = 0, and 1. The zero at 1 has a multiplicity of 2.

𝑥=0 𝑥=1𝑥=1𝑥=−32

c. d.

√−1math!

2-2 Assignment: TX p104, 4-40 EOE