Thurs 11/19 Lesson 5 – 1 Learning Objective: To classify polynomials Hw: 5.1 – 5.2 WS.
-
Upload
ashlee-carr -
Category
Documents
-
view
215 -
download
2
Transcript of Thurs 11/19 Lesson 5 – 1 Learning Objective: To classify polynomials Hw: 5.1 – 5.2 WS.
![Page 1: Thurs 11/19 Lesson 5 – 1 Learning Objective: To classify polynomials Hw: 5.1 – 5.2 WS.](https://reader035.fdocuments.in/reader035/viewer/2022062805/5697bfd11a28abf838caae63/html5/thumbnails/1.jpg)
Homework Log
Thurs
11/19
Lesson 5 – 1
Learning Objective: To classify polynomials
Hw: 5.1 – 5.2 WS
![Page 2: Thurs 11/19 Lesson 5 – 1 Learning Objective: To classify polynomials Hw: 5.1 – 5.2 WS.](https://reader035.fdocuments.in/reader035/viewer/2022062805/5697bfd11a28abf838caae63/html5/thumbnails/2.jpg)
11/19/15 Lesson 5 – 1 Polynomial Functions
Algebra II
![Page 3: Thurs 11/19 Lesson 5 – 1 Learning Objective: To classify polynomials Hw: 5.1 – 5.2 WS.](https://reader035.fdocuments.in/reader035/viewer/2022062805/5697bfd11a28abf838caae63/html5/thumbnails/3.jpg)
To classify polynomials
Learning Objective
![Page 4: Thurs 11/19 Lesson 5 – 1 Learning Objective: To classify polynomials Hw: 5.1 – 5.2 WS.](https://reader035.fdocuments.in/reader035/viewer/2022062805/5697bfd11a28abf838caae63/html5/thumbnails/4.jpg)
5
x + 4
Polynomial DegreeName
0
1
2
3
4
5
Constant
Linear
Quadratic
Cubic
Quartic
Quintic
![Page 5: Thurs 11/19 Lesson 5 – 1 Learning Objective: To classify polynomials Hw: 5.1 – 5.2 WS.](https://reader035.fdocuments.in/reader035/viewer/2022062805/5697bfd11a28abf838caae63/html5/thumbnails/5.jpg)
5
x + 4
Polynomial # of terms Name
1
2
1
3
2
4
Monomial
Binomial
Monomial
Trinomial
Binomial
Polynomial
![Page 6: Thurs 11/19 Lesson 5 – 1 Learning Objective: To classify polynomials Hw: 5.1 – 5.2 WS.](https://reader035.fdocuments.in/reader035/viewer/2022062805/5697bfd11a28abf838caae63/html5/thumbnails/6.jpg)
Arrange the terms by degree in descending numerical order.
Write in standard form & classify by degrees & number of terms.
1. Quadratic Trinomial
Standard Form of a Polynomial Function
![Page 7: Thurs 11/19 Lesson 5 – 1 Learning Objective: To classify polynomials Hw: 5.1 – 5.2 WS.](https://reader035.fdocuments.in/reader035/viewer/2022062805/5697bfd11a28abf838caae63/html5/thumbnails/7.jpg)
2. Quartic Polynomial
3.
Quintic Binomial
Write in standard form & classify by degrees & number of terms
![Page 8: Thurs 11/19 Lesson 5 – 1 Learning Objective: To classify polynomials Hw: 5.1 – 5.2 WS.](https://reader035.fdocuments.in/reader035/viewer/2022062805/5697bfd11a28abf838caae63/html5/thumbnails/8.jpg)
End Behavior
![Page 9: Thurs 11/19 Lesson 5 – 1 Learning Objective: To classify polynomials Hw: 5.1 – 5.2 WS.](https://reader035.fdocuments.in/reader035/viewer/2022062805/5697bfd11a28abf838caae63/html5/thumbnails/9.jpg)
11/19/15 Lesson 5 – 2 Polynomials, Linear
Factors, & ZerosAlgebra II
![Page 10: Thurs 11/19 Lesson 5 – 1 Learning Objective: To classify polynomials Hw: 5.1 – 5.2 WS.](https://reader035.fdocuments.in/reader035/viewer/2022062805/5697bfd11a28abf838caae63/html5/thumbnails/10.jpg)
To analyze the factored form of a polynomial
To write a polynomial function from its zeros
Learning Objective
![Page 11: Thurs 11/19 Lesson 5 – 1 Learning Objective: To classify polynomials Hw: 5.1 – 5.2 WS.](https://reader035.fdocuments.in/reader035/viewer/2022062805/5697bfd11a28abf838caae63/html5/thumbnails/11.jpg)
1. x(x(x – 5) + 3(x – 5)) x(x + 3)(x – 5)Find zeros by = 0 x(x + 3)(x – 5) = 0x = 0, –3, 5
Factor & Find Zeros –15
–23–5
![Page 12: Thurs 11/19 Lesson 5 – 1 Learning Objective: To classify polynomials Hw: 5.1 – 5.2 WS.](https://reader035.fdocuments.in/reader035/viewer/2022062805/5697bfd11a28abf838caae63/html5/thumbnails/12.jpg)
2. x(x(x – 4) + 3(x – 4)) x(x + 3)(x – 4)Find zeros by = 0 x(x + 3)(x – 5) = 0x = 0, –3, 4
Factor & Find Zeros –12
–13–4
![Page 13: Thurs 11/19 Lesson 5 – 1 Learning Objective: To classify polynomials Hw: 5.1 – 5.2 WS.](https://reader035.fdocuments.in/reader035/viewer/2022062805/5697bfd11a28abf838caae63/html5/thumbnails/13.jpg)
3. What is a cubic polynomial function in standard form with zeros –2, 2, and 3?x = –2 x = 2 x = 3x + 2 = 0 x – 2 = 0 x – 3 = 0(x + 2)(x – 2)(x – 3) = 0
Write a Polynomial Function From its Zeros
![Page 14: Thurs 11/19 Lesson 5 – 1 Learning Objective: To classify polynomials Hw: 5.1 – 5.2 WS.](https://reader035.fdocuments.in/reader035/viewer/2022062805/5697bfd11a28abf838caae63/html5/thumbnails/14.jpg)
(x + 2)(x – 2)(x – 3) = 0
– 2 x
–2x 𝑥2
–42x
x
2
– 3 x
–3 𝑥3
12–4x
–4
![Page 15: Thurs 11/19 Lesson 5 – 1 Learning Objective: To classify polynomials Hw: 5.1 – 5.2 WS.](https://reader035.fdocuments.in/reader035/viewer/2022062805/5697bfd11a28abf838caae63/html5/thumbnails/15.jpg)
3. What is a cubic polynomial function in standard form with zeros –2, 2, and 3?x = –2 x = 2 x = 3x + 2 = 0 x – 2 = 0 x – 3 = 0(x + 2)(x – 2)(x – 3) = 0
Write a Polynomial Function From its Zeros
![Page 16: Thurs 11/19 Lesson 5 – 1 Learning Objective: To classify polynomials Hw: 5.1 – 5.2 WS.](https://reader035.fdocuments.in/reader035/viewer/2022062805/5697bfd11a28abf838caae63/html5/thumbnails/16.jpg)
4. What is a cubic polynomial function in standard form with zeros 0, 5, and 5?x = 0 x = 5 x = 5x = 0 x – 5 = 0 x – 5 = 0(x)(x – 5)(x – 5) = 0
Write a Polynomial Function From its Zeros
![Page 17: Thurs 11/19 Lesson 5 – 1 Learning Objective: To classify polynomials Hw: 5.1 – 5.2 WS.](https://reader035.fdocuments.in/reader035/viewer/2022062805/5697bfd11a28abf838caae63/html5/thumbnails/17.jpg)
5. What is a quartic polynomial function in standard form with zeros –2, –2, 2 and 3?x = –2 x = –2 x = 2 x = 3x+2=0 x+2=0 x–2=0 x-3=0(x + 2)(x + 2)(x – 2)(x - 3)=0
Write a Polynomial Function From its Zeros
![Page 18: Thurs 11/19 Lesson 5 – 1 Learning Objective: To classify polynomials Hw: 5.1 – 5.2 WS.](https://reader035.fdocuments.in/reader035/viewer/2022062805/5697bfd11a28abf838caae63/html5/thumbnails/18.jpg)
(x + 2)(x + 2)(x – 2)(x - 3)=0
2 x
2x 𝑥2
42x
x
2
– 3 x
–3x𝑥2
6–2x
x
–2
(𝑥¿¿2−5 𝑥+6)¿
![Page 19: Thurs 11/19 Lesson 5 – 1 Learning Objective: To classify polynomials Hw: 5.1 – 5.2 WS.](https://reader035.fdocuments.in/reader035/viewer/2022062805/5697bfd11a28abf838caae63/html5/thumbnails/19.jpg)
=0
-5 𝑥4
–204
4x
-5 𝑥2 6
6
24x
4 -20x 24 4
𝑥4−𝑥3−10 𝑥2+4 𝑥+24=0
![Page 20: Thurs 11/19 Lesson 5 – 1 Learning Objective: To classify polynomials Hw: 5.1 – 5.2 WS.](https://reader035.fdocuments.in/reader035/viewer/2022062805/5697bfd11a28abf838caae63/html5/thumbnails/20.jpg)
5. What is a quartic polynomial function in standard form with zeros –2, –2, 2 and 3?x = –2 x = –2 x = 2 x = 3x+2=0 x+2=0 x–2=0 x-3=0(x + 2)(x + 2)(x – 2)(x - 3)=0
Write a Polynomial Function From its Zeros
![Page 21: Thurs 11/19 Lesson 5 – 1 Learning Objective: To classify polynomials Hw: 5.1 – 5.2 WS.](https://reader035.fdocuments.in/reader035/viewer/2022062805/5697bfd11a28abf838caae63/html5/thumbnails/21.jpg)
Multiplicity – how many times a factor appears
Even multiplicity – TOUCHES the x-axis, will NOT cross
Odd multiplicity – CROSSES the x-axis
Multiplicity of a Zero
![Page 22: Thurs 11/19 Lesson 5 – 1 Learning Objective: To classify polynomials Hw: 5.1 – 5.2 WS.](https://reader035.fdocuments.in/reader035/viewer/2022062805/5697bfd11a28abf838caae63/html5/thumbnails/22.jpg)
6. What are the zeros of ? What are the multiplicities?
x = 0 (multiplicity 1)x = 3 (multiplicity 4)x = –3 (multiplicity 3)x = –5 (multiplicity 2)
Multiplicity of a Zero
![Page 23: Thurs 11/19 Lesson 5 – 1 Learning Objective: To classify polynomials Hw: 5.1 – 5.2 WS.](https://reader035.fdocuments.in/reader035/viewer/2022062805/5697bfd11a28abf838caae63/html5/thumbnails/23.jpg)
7. What are the zeros of ? What are the multiplicities?
Zeros: x = 0 (multiplicity 2)x = 4 (multiplicity 1)
x = –2 (multiplicity 1)
Multiplicity of a Zero
![Page 24: Thurs 11/19 Lesson 5 – 1 Learning Objective: To classify polynomials Hw: 5.1 – 5.2 WS.](https://reader035.fdocuments.in/reader035/viewer/2022062805/5697bfd11a28abf838caae63/html5/thumbnails/24.jpg)
Write a cubic polynomial function in standard form with roots 4, 2, and – 1.
Ticket Out the Door
![Page 25: Thurs 11/19 Lesson 5 – 1 Learning Objective: To classify polynomials Hw: 5.1 – 5.2 WS.](https://reader035.fdocuments.in/reader035/viewer/2022062805/5697bfd11a28abf838caae63/html5/thumbnails/25.jpg)
Assignment:
Pg. 5.1 – 5.2 WS