Download - Warm-Up 2/20 1. D. Rigor: You will learn how to analyze and graph equations of polynomial functions. Relevance: You will be able to use graphs and equations.

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Page 1: Warm-Up 2/20 1. D. Rigor: You will learn how to analyze and graph equations of polynomial functions. Relevance: You will be able to use graphs and equations.

Warm-Up 2/201.

D

Page 2: Warm-Up 2/20 1. D. Rigor: You will learn how to analyze and graph equations of polynomial functions. Relevance: You will be able to use graphs and equations.
Page 3: Warm-Up 2/20 1. D. Rigor: You will learn how to analyze and graph equations of polynomial functions. Relevance: You will be able to use graphs and equations.

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.

Page 4: Warm-Up 2/20 1. D. Rigor: You will learn how to analyze and graph equations of polynomial functions. Relevance: You will be able to use graphs and equations.

2-2 Polynomial Functions

Page 5: Warm-Up 2/20 1. D. Rigor: You will learn how to analyze and graph equations of polynomial functions. Relevance: You will be able to use graphs and equations.
Page 6: Warm-Up 2/20 1. D. Rigor: You will learn how to analyze and graph equations of polynomial functions. Relevance: You will be able to use graphs and equations.

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.

Page 7: Warm-Up 2/20 1. D. Rigor: You will learn how to analyze and graph equations of polynomial functions. Relevance: You will be able to use graphs and equations.
Page 8: Warm-Up 2/20 1. D. Rigor: You will learn how to analyze and graph equations of polynomial functions. Relevance: You will be able to use graphs and equations.

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

Page 9: Warm-Up 2/20 1. D. Rigor: You will learn how to analyze and graph equations of polynomial functions. Relevance: You will be able to use graphs and equations.
Page 10: Warm-Up 2/20 1. D. Rigor: You will learn how to analyze and graph equations of polynomial functions. Relevance: You will be able to use graphs and equations.

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

π‘₯3βˆ’5 π‘₯2+6 π‘₯=0

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

f has at most 2 turning points.

π‘₯ (π‘₯2βˆ’ 5π‘₯+6 )=0π‘₯ (π‘₯βˆ’ 2 ) (π‘₯βˆ’ 3 )=0f has real zeros at x = 0, 2, and 3.

Page 11: Warm-Up 2/20 1. D. Rigor: You will learn how to analyze and graph equations of polynomial functions. Relevance: You will be able to use graphs and equations.
Page 12: Warm-Up 2/20 1. D. Rigor: You will learn how to analyze and graph equations of polynomial functions. Relevance: You will be able to use graphs and equations.

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

π‘₯4 βˆ’3 π‘₯2βˆ’ 4=0

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

g has at most 3 turning points.

(π‘₯2 )2 βˆ’3 (π‘₯2 ) βˆ’ 4=0

𝑒2 βˆ’3π‘’βˆ’ 4=0

g has real zeros at x = – 2 and 2.

(𝑒+1)(π‘’βˆ’ 4)=0(π‘₯2+1)(π‘₯2βˆ’ 4 )=0

or

π‘₯2=βˆ’1π‘₯=Β±βˆšβˆ’1  

π‘₯2=4π‘₯=Β± 2

Let

Page 13: Warm-Up 2/20 1. D. Rigor: You will learn how to analyze and graph equations of polynomial functions. Relevance: You will be able to use graphs and equations.

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

βˆ’π‘₯4 βˆ’π‘₯3+2 π‘₯2=0

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

h has at most 3 turning points.

βˆ’π‘₯2 (π‘₯2+π‘₯βˆ’ 2 )=0

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

βˆ’π‘₯2(π‘₯βˆ’1)(π‘₯+2)=0 or or

π‘₯=0 π‘₯=1 π‘₯=βˆ’2π‘₯=0

Page 14: Warm-Up 2/20 1. D. Rigor: You will learn how to analyze and graph equations of polynomial functions. Relevance: You will be able to use graphs and equations.

Example 6:

π‘₯ (2π‘₯+3)(π‘₯βˆ’ 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.

π‘₯=0 π‘₯=1π‘₯=1π‘₯=βˆ’32

c. d.

Page 15: Warm-Up 2/20 1. D. Rigor: You will learn how to analyze and graph equations of polynomial functions. Relevance: You will be able to use graphs and equations.

βˆšβˆ’1math!

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