A system for managing rigor Remember rigor is the first letter in rigor mortis.
Warm-Up 2/20 1. D. Rigor: You will learn how to analyze and graph equations of polynomial functions....
-
Upload
kathlyn-morton -
Category
Documents
-
view
214 -
download
0
Transcript of Warm-Up 2/20 1. D. Rigor: You will learn how to analyze and graph equations of polynomial functions....
![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.](https://reader036.fdocuments.us/reader036/viewer/2022062804/5697bf8a1a28abf838c8ab09/html5/thumbnails/1.jpg)
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.](https://reader036.fdocuments.us/reader036/viewer/2022062804/5697bf8a1a28abf838c8ab09/html5/thumbnails/2.jpg)
![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.](https://reader036.fdocuments.us/reader036/viewer/2022062804/5697bf8a1a28abf838c8ab09/html5/thumbnails/3.jpg)
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.](https://reader036.fdocuments.us/reader036/viewer/2022062804/5697bf8a1a28abf838c8ab09/html5/thumbnails/4.jpg)
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.](https://reader036.fdocuments.us/reader036/viewer/2022062804/5697bf8a1a28abf838c8ab09/html5/thumbnails/5.jpg)
![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.](https://reader036.fdocuments.us/reader036/viewer/2022062804/5697bf8a1a28abf838c8ab09/html5/thumbnails/6.jpg)
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.](https://reader036.fdocuments.us/reader036/viewer/2022062804/5697bf8a1a28abf838c8ab09/html5/thumbnails/7.jpg)
![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.](https://reader036.fdocuments.us/reader036/viewer/2022062804/5697bf8a1a28abf838c8ab09/html5/thumbnails/8.jpg)
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.](https://reader036.fdocuments.us/reader036/viewer/2022062804/5697bf8a1a28abf838c8ab09/html5/thumbnails/9.jpg)
![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.](https://reader036.fdocuments.us/reader036/viewer/2022062804/5697bf8a1a28abf838c8ab09/html5/thumbnails/10.jpg)
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.
![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.](https://reader036.fdocuments.us/reader036/viewer/2022062804/5697bf8a1a28abf838c8ab09/html5/thumbnails/11.jpg)
![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.](https://reader036.fdocuments.us/reader036/viewer/2022062804/5697bf8a1a28abf838c8ab09/html5/thumbnails/12.jpg)
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
![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.](https://reader036.fdocuments.us/reader036/viewer/2022062804/5697bf8a1a28abf838c8ab09/html5/thumbnails/13.jpg)
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
![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.](https://reader036.fdocuments.us/reader036/viewer/2022062804/5697bf8a1a28abf838c8ab09/html5/thumbnails/14.jpg)
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.
![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.](https://reader036.fdocuments.us/reader036/viewer/2022062804/5697bf8a1a28abf838c8ab09/html5/thumbnails/15.jpg)
√−1math!
2-2 Assignment: TX p104, 4-40 EOE