Warm-Up 2/20 1. D. Rigor: You will learn how to analyze and graph equations of polynomial functions....
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Transcript of Warm-Up 2/20 1. D. Rigor: You will learn how to analyze and graph equations of polynomial functions....
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