CHAPTER 2 RevIEw
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Transcript of CHAPTER 2 RevIEw
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CHAPTER 2 RevIEw
precalculus
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y = (x+2)2
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y = (x-2)2 -1
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y = -(x+1)2 + 3
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4) The number of horsepower H required to overcome wind drag on a certain car is approximated by H(s) = 0.002s2 + 0.05s - 0.029 , 0 < s < 100 where s is the speed of the car in miles per hour.
a) Use a graphing calculator to graph.
b) Estimate the maximum speed of the car if the power required to overcome wind drag is not to exceed 10 horsepower. Round your answer to the nearest tenth.
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4) The number of horsepower H required to overcome wind drag on a certain car is approximated by H(s) = 0.002s2 + 0.05s - 0.029 , 0 < s < 100 where s is the speed of the car in miles per hour.
a) Use a graphing calculator to graph.
b) Estimate the maximum speed of the car if the power required to overcome wind drag is not to exceed 10 horsepower. Round your answer to the nearest tenth.
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4) The number of horsepower H required to overcome wind drag on a certain car is approximated by H(s) = 0.002s2 + 0.05s - 0.029 , 0 < s < 100 where s is the speed of the car in miles per hour.
a) Use a graphing calculator to graph.
b) Estimate the maximum speed of the car if the power required to overcome wind drag is not to exceed 10 horsepower. Round your answer to the nearest tenth.
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4) The number of horsepower H required to overcome wind drag on a certain car is approximated by H(s) = 0.002s2 + 0.05s - 0.029 , 0 < s < 100 where s is the speed of the car in miles per hour.
a) Use a graphing calculator to graph.
b) Estimate the maximum speed of the car if the power required to overcome wind drag is not to exceed 10 horsepower. Round your answer to the nearest tenth.
59.4 MPH
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5) f(x) = x2 - 16
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5) f(x) = x2 - 16 = (x )(x )
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5) f(x) = x2 - 16 = (x - 4)(x + 4)
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5) f(x) = x2 - 16 = (x - 4)(x + 4)
zeros: 4, -4
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6) f(x) = x2 + 12x + 36
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6) f(x) = x2 + 12x + 36 = (x )(x )
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6) f(x) = x2 + 12x + 36 = (x + 6)(x + 6)
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6) f(x) = x2 + 12x + 36 = (x + 6)(x + 6)
zeros: -6, -6
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7) f(x) = 2x2 - 14x + 24
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7) f(x) = 2x2 - 14x + 24 = 2( )
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7) f(x) = 2x2 - 14x + 24 = 2(x2 - 7x + 12)
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7) f(x) = 2x2 - 14x + 24 = 2(x2 - 7x + 12) = 2(x )(x )
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7) f(x) = 2x2 - 14x + 24 = 2(x2 - 7x + 12) = 2(x - 4)(x - 3)
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7) f(x) = 2x2 - 14x + 24 = 2(x2 - 7x + 12) = 2(x - 4)(x - 3) zeros: 4, 3
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8) f(x) = x4 - x3 - 20x2
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8) f(x) = x4 - x3 - 20x2
= x2( )
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8) f(x) = x4 - x3 - 20x2
= x2(x2 - x - 20x)
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8) f(x) = x4 - x3 - 20x2
= x2(x2 - x - 20x) = x2(x )(x )
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8) f(x) = x4 - x3 - 20x2
= x2(x2 - x - 20x) = x2(x + 4)(x - 5)
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8) f(x) = x4 - x3 - 20x2
= x2(x2 - x - 20x) = x2(x + 4)(x - 5) = (x)(x)(x + 4)(x - 5)
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8) f(x) = x4 - x3 - 20x2
= x2(x2 - x - 20x) = x2(x + 4)(x - 5) = (x)(x)(x + 4)(x - 5) zeros: 0, 0, -4, 5
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Find a polynomial with the following zeros.9) -7, 2
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Find a polynomial with the following zeros.9) -7, 2
(x - -7)(x - 2)
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Find a polynomial with the following zeros.9) -7, 2
(x - -7)(x - 2)
(x + 7)(x - 2)
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Find a polynomial with the following zeros.9) -7, 2
(x - -7)(x - 2)
(x + 7)(x - 2)x2 - 2x + 7x - 14
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Find a polynomial with the following zeros.9) -7, 2
(x - -7)(x - 2)
(x + 7)(x - 2)x2 - 2x + 7x - 14x2 + 5x - 14
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10) 0, 4
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10) 0, 4(x - 0)(x - 4)
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10) 0, 4(x - 0)(x - 4)x(x - 4)
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10) 0, 4(x - 0)(x - 4)x(x - 4)x2 - 4x
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What does the graph of each function look like? (circle two for each)11) f(x) = -x2 + 6x + 9 rises to the left rises to the right
falls to the left falls to the right
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What does the graph of each function look like? (circle two for each)11) f(x) = -x2 + 6x + 9 rises to the left rises to the right
falls to the left falls to the right
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What does the graph of each function look like? (circle two for each)11) f(x) = -x2 + 6x + 9 rises to the left rises to the right
falls to the left falls to the right
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12) f(x) = 0.5x3 + 2x rises to the left rises to the rightfalls to the left falls to the right
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12) f(x) = 0.5x3 + 2x rises to the left rises to the rightfalls to the left falls to the right
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12) f(x) = 0.5x3 + 2x rises to the left rises to the rightfalls to the left falls to the right
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13) f(x) = 6(x4 + 3x2 + 2) rises to the left rises to the rightfalls to the left falls to the right
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13) f(x) = 6(x4 + 3x2 + 2) rises to the left rises to the rightfalls to the left falls to the right
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13) f(x) = 6(x4 + 3x2 + 2) rises to the left rises to the rightfalls to the left falls to the right
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14) f(x) = -x5 - 7x + 10 rises to the left rises to the rightfalls to the left falls to the right
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14) f(x) = -x5 - 7x + 10 rises to the left rises to the rightfalls to the left falls to the right
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14) f(x) = -x5 - 7x + 10 rises to the left rises to the rightfalls to the left falls to the right
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Use long division to simplify.15) (2x3 - 3x2 - 50x + 75) / (2x - 3)
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Use long division to simplify.15) (2x3 - 3x2 - 50x + 75) / (2x - 3)
2x - 3 2x3 - 3x2 - 50x + 75
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Use long division to simplify.15) (2x3 - 3x2 - 50x + 75) / (2x - 3)
x2
2x - 3 2x3 - 3x2 - 50x + 75
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Use long division to simplify.15) (2x3 - 3x2 - 50x + 75) / (2x - 3)
x2
2x - 3 2x3 - 3x2 - 50x + 75 2x3 - 3x2
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Use long division to simplify.15) (2x3 - 3x2 - 50x + 75) / (2x - 3)
x2
2x - 3 2x3 - 3x2 - 50x + 75 2x3 - 3x2
0 0
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Use long division to simplify.15) (2x3 - 3x2 - 50x + 75) / (2x - 3)
x2
2x - 3 2x3 - 3x2 - 50x + 75 2x3 - 3x2
0 0 - 50x + 75
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Use long division to simplify.15) (2x3 - 3x2 - 50x + 75) / (2x - 3)
x2 - 252x - 3 2x3 - 3x2 - 50x + 75 2x3 - 3x2
0 0 - 50x + 75
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Use long division to simplify.15) (2x3 - 3x2 - 50x + 75) / (2x - 3)
x2 - 252x - 3 2x3 - 3x2 - 50x + 75 2x3 - 3x2
0 0 - 50x + 75 - 50x + 75
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Use long division to simplify.15) (2x3 - 3x2 - 50x + 75) / (2x - 3)
x2 - 252x - 3 2x3 - 3x2 - 50x + 75 2x3 - 3x2
0 0 - 50x + 75 - 50x + 75 0 0
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Use long division to simplify.15) (2x3 - 3x2 - 50x + 75) / (2x - 3)
x2 - 252x - 3 2x3 - 3x2 - 50x + 75 2x3 - 3x2
0 0 - 50x + 75 - 50x + 75 0 0
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Use synthetic division to simplify.16) (3x3 - 17x2 + 15x - 25) / (x - 5)
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Use synthetic division to simplify.16) (3x3 - 17x2 + 15x - 25) / (x - 5)
3 -17 15 -25
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Use synthetic division to simplify.16) (3x3 - 17x2 + 15x - 25) / (x - 5)
5 3 -17 15 -25
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Use synthetic division to simplify.16) (3x3 - 17x2 + 15x - 25) / (x - 5)
5 3 -17 15 -25 3
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Use synthetic division to simplify.16) (3x3 - 17x2 + 15x - 25) / (x - 5)
5 3 -17 15 -25 15 3
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Use synthetic division to simplify.16) (3x3 - 17x2 + 15x - 25) / (x - 5)
5 3 -17 15 -25 15 3 -2
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Use synthetic division to simplify.16) (3x3 - 17x2 + 15x - 25) / (x - 5)
5 3 -17 15 -25 15 -10 3 -2
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Use synthetic division to simplify.16) (3x3 - 17x2 + 15x - 25) / (x - 5)
5 3 -17 15 -25 15 -10 3 -2 5
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Use synthetic division to simplify.16) (3x3 - 17x2 + 15x - 25) / (x - 5)
5 3 -17 15 -25 15 -10 25 3 -2 5
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Use synthetic division to simplify.16) (3x3 - 17x2 + 15x - 25) / (x - 5)
5 3 -17 15 -25 15 -10 25 3 -2 5 0
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Use synthetic division to simplify.16) (3x3 - 17x2 + 15x - 25) / (x - 5)
5 3 -17 15 -25 15 -10 25 3 -2 5 0
3x2 - 2x + 5
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17) (2x3 + 14x2 - 20x + 7) / (x + 6)
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17) (2x3 + 14x2 - 20x + 7) / (x + 6)
2 14 -20 7
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17) (2x3 + 14x2 - 20x + 7) / (x + 6)
-6 2 14 -20 7
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17) (2x3 + 14x2 - 20x + 7) / (x + 6)
-6 2 14 -20 7 -12 -12 192 2 2 -32 199
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17) (2x3 + 14x2 - 20x + 7) / (x + 6)
-6 2 14 -20 7 -12 -12 192 2 2 -32 199
2x2 + 2x - 32 + 199 x+6
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Write in completely factored form. Then find all zeros.18) f(x) = x3 + 4x2 - 25x - 28 Hint: (x - 4) is a factor
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Write in completely factored form. Then find all zeros.18) f(x) = x3 + 4x2 - 25x - 28 Hint: (x - 4) is a factor
1 4 -25 -28
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Write in completely factored form. Then find all zeros.18) f(x) = x3 + 4x2 - 25x - 28 Hint: (x - 4) is a factor
4 1 4 -25 -28
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Write in completely factored form. Then find all zeros.18) f(x) = x3 + 4x2 - 25x - 28 Hint: (x - 4) is a factor
4 1 4 -25 -28 4 32 28 1 8 7 0
![Page 84: CHAPTER 2 RevIEw](https://reader031.fdocuments.net/reader031/viewer/2022020920/5681613f550346895dd0a936/html5/thumbnails/84.jpg)
Write in completely factored form. Then find all zeros.18) f(x) = x3 + 4x2 - 25x - 28 Hint: (x - 4) is a factor
4 1 4 -25 -28 4 32 28 1 8 7 0
x2 + 8x + 7
![Page 85: CHAPTER 2 RevIEw](https://reader031.fdocuments.net/reader031/viewer/2022020920/5681613f550346895dd0a936/html5/thumbnails/85.jpg)
Write in completely factored form. Then find all zeros.18) f(x) = x3 + 4x2 - 25x - 28 Hint: (x - 4) is a factor
4 1 4 -25 -28 4 32 28 1 8 7 0
x2 + 8x + 7 (x + 1)(x + 7)
![Page 86: CHAPTER 2 RevIEw](https://reader031.fdocuments.net/reader031/viewer/2022020920/5681613f550346895dd0a936/html5/thumbnails/86.jpg)
Write in completely factored form. Then find all zeros.18) f(x) = x3 + 4x2 - 25x - 28 Hint: (x - 4) is a factor
4 1 4 -25 -28 4 32 28 1 8 7 0
x2 + 8x + 7 (x + 1)(x + 7)
(x - 4)(x + 1)(x + 7)
![Page 87: CHAPTER 2 RevIEw](https://reader031.fdocuments.net/reader031/viewer/2022020920/5681613f550346895dd0a936/html5/thumbnails/87.jpg)
Write in completely factored form. Then find all zeros.18) f(x) = x3 + 4x2 - 25x - 28 Hint: (x - 4) is a factor
4 1 4 -25 -28 4 32 28 1 8 7 0
x2 + 8x + 7 (x + 1)(x + 7)
(x - 4)(x + 1)(x + 7) zeros: 4, -1, -7
![Page 88: CHAPTER 2 RevIEw](https://reader031.fdocuments.net/reader031/viewer/2022020920/5681613f550346895dd0a936/html5/thumbnails/88.jpg)
19) f(x) = x4 - 4x3 - 7x2 + 22x + 24 Hint: (x + 2) and (x - 3) are factors
![Page 89: CHAPTER 2 RevIEw](https://reader031.fdocuments.net/reader031/viewer/2022020920/5681613f550346895dd0a936/html5/thumbnails/89.jpg)
19) f(x) = x4 - 4x3 - 7x2 + 22x + 24 Hint: (x + 2) and (x - 3) are factors
1 -4 -7 22 24
![Page 90: CHAPTER 2 RevIEw](https://reader031.fdocuments.net/reader031/viewer/2022020920/5681613f550346895dd0a936/html5/thumbnails/90.jpg)
19) f(x) = x4 - 4x3 - 7x2 + 22x + 24 Hint: (x + 2) and (x - 3) are factors
3 1 -4 -7 22 24 3 -3 -30 -24 1 -1 -10 -8 0
![Page 91: CHAPTER 2 RevIEw](https://reader031.fdocuments.net/reader031/viewer/2022020920/5681613f550346895dd0a936/html5/thumbnails/91.jpg)
19) f(x) = x4 - 4x3 - 7x2 + 22x + 24 Hint: (x + 2) and (x - 3) are factors
3 1 -4 -7 22 24 3 -3 -30 -24 1 -1 -10 -8 0 x3 - x2 - 10x - 8
![Page 92: CHAPTER 2 RevIEw](https://reader031.fdocuments.net/reader031/viewer/2022020920/5681613f550346895dd0a936/html5/thumbnails/92.jpg)
19) f(x) = x4 - 4x3 - 7x2 + 22x + 24 Hint: (x + 2) and (x - 3) are factors
3 1 -4 -7 22 24 3 -3 -30 -24 1 -1 -10 -8 0 x3 - x2 - 10x - 8 1 -1 -10 -8
![Page 93: CHAPTER 2 RevIEw](https://reader031.fdocuments.net/reader031/viewer/2022020920/5681613f550346895dd0a936/html5/thumbnails/93.jpg)
19) f(x) = x4 - 4x3 - 7x2 + 22x + 24 Hint: (x + 2) and (x - 3) are factors
3 1 -4 -7 22 24 3 -3 -30 -24 1 -1 -10 -8 0 x3 - x2 - 10x - 8 -2 1 -1 -10 -8
![Page 94: CHAPTER 2 RevIEw](https://reader031.fdocuments.net/reader031/viewer/2022020920/5681613f550346895dd0a936/html5/thumbnails/94.jpg)
19) f(x) = x4 - 4x3 - 7x2 + 22x + 24 Hint: (x + 2) and (x - 3) are factors
3 1 -4 -7 22 24 3 -3 -30 -24 1 -1 -10 -8 0 x3 - x2 - 10x - 8 -2 1 -1 -10 -8 -2 6 8 1 -3 -4 0
![Page 95: CHAPTER 2 RevIEw](https://reader031.fdocuments.net/reader031/viewer/2022020920/5681613f550346895dd0a936/html5/thumbnails/95.jpg)
19) f(x) = x4 - 4x3 - 7x2 + 22x + 24 Hint: (x + 2) and (x - 3) are factors
3 1 -4 -7 22 24 3 -3 -30 -24 1 -1 -10 -8 0 x3 - x2 - 10x - 8 -2 1 -1 -10 -8 -2 6 8 1 -3 -4 0 x2 - 3x - 4
![Page 96: CHAPTER 2 RevIEw](https://reader031.fdocuments.net/reader031/viewer/2022020920/5681613f550346895dd0a936/html5/thumbnails/96.jpg)
19) f(x) = x4 - 4x3 - 7x2 + 22x + 24 Hint: (x + 2) and (x - 3) are factors
3 1 -4 -7 22 24 3 -3 -30 -24 1 -1 -10 -8 0 x3 - x2 - 10x - 8 -2 1 -1 -10 -8 -2 6 8 1 -3 -4 0 x2 - 3x - 4 (x - 4)(x + 1)
![Page 97: CHAPTER 2 RevIEw](https://reader031.fdocuments.net/reader031/viewer/2022020920/5681613f550346895dd0a936/html5/thumbnails/97.jpg)
19) f(x) = x4 - 4x3 - 7x2 + 22x + 24 Hint: (x + 2) and (x - 3) are factors
3 1 -4 -7 22 24 3 -3 -30 -24 1 -1 -10 -8 0 x3 - x2 - 10x - 8 -2 1 -1 -10 -8 -2 6 8 1 -3 -4 0 x2 - 3x - 4 (x - 4)(x + 1) (x - 4)(x + 1)(x + 2)(x - 3)
![Page 98: CHAPTER 2 RevIEw](https://reader031.fdocuments.net/reader031/viewer/2022020920/5681613f550346895dd0a936/html5/thumbnails/98.jpg)
19) f(x) = x4 - 4x3 - 7x2 + 22x + 24 Hint: (x + 2) and (x - 3) are factors
3 1 -4 -7 22 24 3 -3 -30 -24 1 -1 -10 -8 0 x3 - x2 - 10x - 8 -2 1 -1 -10 -8 -2 6 8 1 -3 -4 0 x2 - 3x - 4 (x - 4)(x + 1) (x - 4)(x + 1)(x + 2)(x - 3) zeros: 4, -1, -2, 3
![Page 99: CHAPTER 2 RevIEw](https://reader031.fdocuments.net/reader031/viewer/2022020920/5681613f550346895dd0a936/html5/thumbnails/99.jpg)
Write each complex number in standard form.20) (3 + 2i) + (5 + i)
![Page 100: CHAPTER 2 RevIEw](https://reader031.fdocuments.net/reader031/viewer/2022020920/5681613f550346895dd0a936/html5/thumbnails/100.jpg)
Write each complex number in standard form.20) (3 + 2i) + (5 + i)
8 + 3i
![Page 101: CHAPTER 2 RevIEw](https://reader031.fdocuments.net/reader031/viewer/2022020920/5681613f550346895dd0a936/html5/thumbnails/101.jpg)
21) (3 + 2i)(5 + i)
![Page 102: CHAPTER 2 RevIEw](https://reader031.fdocuments.net/reader031/viewer/2022020920/5681613f550346895dd0a936/html5/thumbnails/102.jpg)
21) (3 + 2i)(5 + i)15 + 3i + 10i + 2i2
![Page 103: CHAPTER 2 RevIEw](https://reader031.fdocuments.net/reader031/viewer/2022020920/5681613f550346895dd0a936/html5/thumbnails/103.jpg)
21) (3 + 2i)(5 + i)15 + 3i + 10i + 2i2
15 + 13i + 2i2
![Page 104: CHAPTER 2 RevIEw](https://reader031.fdocuments.net/reader031/viewer/2022020920/5681613f550346895dd0a936/html5/thumbnails/104.jpg)
21) (3 + 2i)(5 + i)15 + 3i + 10i + 2i2
15 + 13i + 2i2
15 + 13i + 2(-1)
![Page 105: CHAPTER 2 RevIEw](https://reader031.fdocuments.net/reader031/viewer/2022020920/5681613f550346895dd0a936/html5/thumbnails/105.jpg)
21) (3 + 2i)(5 + i)15 + 3i + 10i + 2i2
15 + 13i + 2i2
15 + 13i + 2(-1)13 + 13i
![Page 106: CHAPTER 2 RevIEw](https://reader031.fdocuments.net/reader031/viewer/2022020920/5681613f550346895dd0a936/html5/thumbnails/106.jpg)
22) (3 + 2i) (5 + i)
![Page 107: CHAPTER 2 RevIEw](https://reader031.fdocuments.net/reader031/viewer/2022020920/5681613f550346895dd0a936/html5/thumbnails/107.jpg)
22) (3 + 2i) * (5 - i) (5 + i) * (5 - i)
![Page 108: CHAPTER 2 RevIEw](https://reader031.fdocuments.net/reader031/viewer/2022020920/5681613f550346895dd0a936/html5/thumbnails/108.jpg)
22) (3 + 2i) * (5 - i) = 15 - 3i + 10i - 2i2
(5 + i) * (5 - i) = 25 + 5i - 5i - i2
![Page 109: CHAPTER 2 RevIEw](https://reader031.fdocuments.net/reader031/viewer/2022020920/5681613f550346895dd0a936/html5/thumbnails/109.jpg)
22) (3 + 2i) * (5 - i) = 15 - 3i + 10i - 2i2 = 15 + 7i -2(-1) (5 + i) * (5 - i) = 25 + 5i - 5i - i2
![Page 110: CHAPTER 2 RevIEw](https://reader031.fdocuments.net/reader031/viewer/2022020920/5681613f550346895dd0a936/html5/thumbnails/110.jpg)
22) (3 + 2i) * (5 - i) = 15 - 3i + 10i - 2i2 = 15 + 7i -2(-1) (5 + i) * (5 - i) = 25 + 5i - 5i - i2 = 25 - (-1)
![Page 111: CHAPTER 2 RevIEw](https://reader031.fdocuments.net/reader031/viewer/2022020920/5681613f550346895dd0a936/html5/thumbnails/111.jpg)
22) (3 + 2i) * (5 - i) = 15 - 3i + 10i - 2i2 = 15 + 7i -2(-1) = (5 + i) * (5 - i) = 25 + 5i - 5i - i2 = 25 - (-1)
17 + 7i 26
![Page 112: CHAPTER 2 RevIEw](https://reader031.fdocuments.net/reader031/viewer/2022020920/5681613f550346895dd0a936/html5/thumbnails/112.jpg)
22) (3 + 2i) * (5 - i) = 15 - 3i + 10i - 2i2 = 15 + 7i -2(-1) = (5 + i) * (5 - i) = 25 + 5i - 5i - i2 = 25 - (-1)
17 + 7i 26
17 + 7 i26 26
![Page 113: CHAPTER 2 RevIEw](https://reader031.fdocuments.net/reader031/viewer/2022020920/5681613f550346895dd0a936/html5/thumbnails/113.jpg)
Find all zeros. Then rewrite the function in completely factored form.23) f(x) = x2 - 10x + 6
![Page 114: CHAPTER 2 RevIEw](https://reader031.fdocuments.net/reader031/viewer/2022020920/5681613f550346895dd0a936/html5/thumbnails/114.jpg)
Find all zeros. Then rewrite the function in completely factored form.23) f(x) = x2 - 10x + 6
A = 1B = -10C = 6
![Page 115: CHAPTER 2 RevIEw](https://reader031.fdocuments.net/reader031/viewer/2022020920/5681613f550346895dd0a936/html5/thumbnails/115.jpg)
Find all zeros. Then rewrite the function in completely factored form.23) f(x) = x2 - 10x + 6
A = 1B = -10C = 6
![Page 116: CHAPTER 2 RevIEw](https://reader031.fdocuments.net/reader031/viewer/2022020920/5681613f550346895dd0a936/html5/thumbnails/116.jpg)
Find all zeros. Then rewrite the function in completely factored form.23) f(x) = x2 - 10x + 6
A = 1B = -10C = 6
![Page 117: CHAPTER 2 RevIEw](https://reader031.fdocuments.net/reader031/viewer/2022020920/5681613f550346895dd0a936/html5/thumbnails/117.jpg)
Find all zeros. Then rewrite the function in completely factored form.23) f(x) = x2 - 10x + 6
A = 1B = -10C = 6
![Page 118: CHAPTER 2 RevIEw](https://reader031.fdocuments.net/reader031/viewer/2022020920/5681613f550346895dd0a936/html5/thumbnails/118.jpg)
Find all zeros. Then rewrite the function in completely factored form.23) f(x) = x2 - 10x + 6
A = 1B = -10C = 6
![Page 119: CHAPTER 2 RevIEw](https://reader031.fdocuments.net/reader031/viewer/2022020920/5681613f550346895dd0a936/html5/thumbnails/119.jpg)
Find all zeros. Then rewrite the function in completely factored form.23) f(x) = x2 - 10x + 6
A = 1B = -10C = 6
=
![Page 120: CHAPTER 2 RevIEw](https://reader031.fdocuments.net/reader031/viewer/2022020920/5681613f550346895dd0a936/html5/thumbnails/120.jpg)
Find all zeros. Then rewrite the function in completely factored form.23) f(x) = x2 - 10x + 6
A = 1B = -10C = 6
=
![Page 121: CHAPTER 2 RevIEw](https://reader031.fdocuments.net/reader031/viewer/2022020920/5681613f550346895dd0a936/html5/thumbnails/121.jpg)
24) f(x) = x2 + 2x + 4
![Page 122: CHAPTER 2 RevIEw](https://reader031.fdocuments.net/reader031/viewer/2022020920/5681613f550346895dd0a936/html5/thumbnails/122.jpg)
24) f(x) = x2 + 2x + 4
Quadratic Formula
![Page 123: CHAPTER 2 RevIEw](https://reader031.fdocuments.net/reader031/viewer/2022020920/5681613f550346895dd0a936/html5/thumbnails/123.jpg)
24) f(x) = x2 + 2x + 4
Quadratic Formula ---------> Magic Happens
![Page 124: CHAPTER 2 RevIEw](https://reader031.fdocuments.net/reader031/viewer/2022020920/5681613f550346895dd0a936/html5/thumbnails/124.jpg)
24) f(x) = x2 + 2x + 4
Quadratic Formula ---------> Magic Happens ------------>
![Page 125: CHAPTER 2 RevIEw](https://reader031.fdocuments.net/reader031/viewer/2022020920/5681613f550346895dd0a936/html5/thumbnails/125.jpg)
24) f(x) = x2 + 2x + 4
Quadratic Formula ---------> Magic Happens ------------>
![Page 126: CHAPTER 2 RevIEw](https://reader031.fdocuments.net/reader031/viewer/2022020920/5681613f550346895dd0a936/html5/thumbnails/126.jpg)
25) f(x) = 3x4 - 4x3 + 7x2 + 10x - 4
![Page 127: CHAPTER 2 RevIEw](https://reader031.fdocuments.net/reader031/viewer/2022020920/5681613f550346895dd0a936/html5/thumbnails/127.jpg)
25) f(x) = 3x4 - 4x3 + 7x2 + 10x - 4
![Page 128: CHAPTER 2 RevIEw](https://reader031.fdocuments.net/reader031/viewer/2022020920/5681613f550346895dd0a936/html5/thumbnails/128.jpg)
25) f(x) = 3x4 - 4x3 + 7x2 + 10x - 4
-1 3 -4 7 10 -4 -3 7 -14 4 3 -7 14 -4 0 3x3 - 7x2 + 14x - 4
![Page 129: CHAPTER 2 RevIEw](https://reader031.fdocuments.net/reader031/viewer/2022020920/5681613f550346895dd0a936/html5/thumbnails/129.jpg)
25) f(x) = 3x4 - 4x3 + 7x2 + 10x - 4
-1 3 -4 7 10 -4 -3 7 -14 4 3 -7 14 -4 0 3x3 - 7x2 + 14x - 4
![Page 130: CHAPTER 2 RevIEw](https://reader031.fdocuments.net/reader031/viewer/2022020920/5681613f550346895dd0a936/html5/thumbnails/130.jpg)
25) f(x) = 3x4 - 4x3 + 7x2 + 10x - 4
-1 3 -4 7 10 -4 -3 7 -14 4 3 -7 14 -4 0 3x3 - 7x2 + 14x - 4
3x3 - 7x2 + 14x - 4
![Page 131: CHAPTER 2 RevIEw](https://reader031.fdocuments.net/reader031/viewer/2022020920/5681613f550346895dd0a936/html5/thumbnails/131.jpg)
25) f(x) = 3x4 - 4x3 + 7x2 + 10x - 4
-1 3 -4 7 10 -4 1/3 3 -7 14 -4 -3 7 -14 4 1 -2 4 3 -7 14 -4 0 3 -6 12 0 3x3 - 7x2 + 14x - 4 3x2 - 6x + 12
3x3 - 7x2 + 14x - 4
![Page 132: CHAPTER 2 RevIEw](https://reader031.fdocuments.net/reader031/viewer/2022020920/5681613f550346895dd0a936/html5/thumbnails/132.jpg)
25) f(x) = 3x4 - 4x3 + 7x2 + 10x - 4
-1 3 -4 7 10 -4 1/3 3 -7 14 -4 -3 7 -14 4 1 -2 4 3 -7 14 -4 0 3 -6 12 0 3x3 - 7x2 + 14x - 4 3x2 - 6x + 12
Quadratic Formula
3x3 - 7x2 + 14x - 4
![Page 133: CHAPTER 2 RevIEw](https://reader031.fdocuments.net/reader031/viewer/2022020920/5681613f550346895dd0a936/html5/thumbnails/133.jpg)
25) f(x) = 3x4 - 4x3 + 7x2 + 10x - 4
-1 3 -4 7 10 -4 1/3 3 -7 14 -4 -3 7 -14 4 1 -2 4 3 -7 14 -4 0 3 -6 12 0 3x3 - 7x2 + 14x - 4 3x2 - 6x + 12
Quadratic Formula -------> Magic Happens
3x3 - 7x2 + 14x - 4
![Page 134: CHAPTER 2 RevIEw](https://reader031.fdocuments.net/reader031/viewer/2022020920/5681613f550346895dd0a936/html5/thumbnails/134.jpg)
25) f(x) = 3x4 - 4x3 + 7x2 + 10x - 4
-1 3 -4 7 10 -4 1/3 3 -7 14 -4 -3 7 -14 4 1 -2 4 3 -7 14 -4 0 3 -6 12 0 3x3 - 7x2 + 14x - 4 3x2 - 6x + 12
Quadratic Formula -------> Magic Happens ------->
3x3 - 7x2 + 14x - 4x = x =
![Page 135: CHAPTER 2 RevIEw](https://reader031.fdocuments.net/reader031/viewer/2022020920/5681613f550346895dd0a936/html5/thumbnails/135.jpg)
25) f(x) = 3x4 - 4x3 + 7x2 + 10x - 4
-1 3 -4 7 10 -4 1/3 3 -7 14 -4 -3 7 -14 4 1 -2 4 3 -7 14 -4 0 3 -6 12 0 3x3 - 7x2 + 14x - 4 3x2 - 6x + 12
Quadratic Formula -------> Magic Happens ------->
3x3 - 7x2 + 14x - 4x = x =
![Page 136: CHAPTER 2 RevIEw](https://reader031.fdocuments.net/reader031/viewer/2022020920/5681613f550346895dd0a936/html5/thumbnails/136.jpg)
26) f(x) = x3 - 4x2 + 6x - 4
![Page 137: CHAPTER 2 RevIEw](https://reader031.fdocuments.net/reader031/viewer/2022020920/5681613f550346895dd0a936/html5/thumbnails/137.jpg)
26) f(x) = x3 - 4x2 + 6x - 4
![Page 138: CHAPTER 2 RevIEw](https://reader031.fdocuments.net/reader031/viewer/2022020920/5681613f550346895dd0a936/html5/thumbnails/138.jpg)
26) f(x) = x3 - 4x2 + 6x - 4
2, ____, ____
![Page 139: CHAPTER 2 RevIEw](https://reader031.fdocuments.net/reader031/viewer/2022020920/5681613f550346895dd0a936/html5/thumbnails/139.jpg)
26) f(x) = x3 - 4x2 + 6x - 4
2, ____, ____
Synthetic Division
![Page 140: CHAPTER 2 RevIEw](https://reader031.fdocuments.net/reader031/viewer/2022020920/5681613f550346895dd0a936/html5/thumbnails/140.jpg)
26) f(x) = x3 - 4x2 + 6x - 4
2, ____, ____
Synthetic Division ------> x2 - 2x + 2
![Page 141: CHAPTER 2 RevIEw](https://reader031.fdocuments.net/reader031/viewer/2022020920/5681613f550346895dd0a936/html5/thumbnails/141.jpg)
26) f(x) = x3 - 4x2 + 6x - 4
2, ____, ____
Synthetic Division ------> x2 - 2x + 2 ------> Quadratic Formula
![Page 142: CHAPTER 2 RevIEw](https://reader031.fdocuments.net/reader031/viewer/2022020920/5681613f550346895dd0a936/html5/thumbnails/142.jpg)
26) f(x) = x3 - 4x2 + 6x - 4
2, 1 + i, 1 - i
Synthetic Division ------> x2 - 2x + 2 ------> Quadratic Formula
![Page 143: CHAPTER 2 RevIEw](https://reader031.fdocuments.net/reader031/viewer/2022020920/5681613f550346895dd0a936/html5/thumbnails/143.jpg)
26) f(x) = x3 - 4x2 + 6x - 4
2, 1 + i, 1 - i
(x - 2)(x - 1 - i)(x - 1 + i)
Synthetic Division ------> x2 - 2x + 2 ------> Quadratic Formula
![Page 144: CHAPTER 2 RevIEw](https://reader031.fdocuments.net/reader031/viewer/2022020920/5681613f550346895dd0a936/html5/thumbnails/144.jpg)
Find a polynomial with the following zeros.27) 2 + 3i, 2 - 3i
(x - (2+3i))(x - (2 - 3i))(x - 2 - 3i)(x - 2 + 3i)x2 - 2x + 3ix
![Page 145: CHAPTER 2 RevIEw](https://reader031.fdocuments.net/reader031/viewer/2022020920/5681613f550346895dd0a936/html5/thumbnails/145.jpg)
Find a polynomial with the following zeros.27) 2 + 3i, 2 - 3i
(x - (2+3i))(x - (2 - 3i))(x - 2 - 3i)(x - 2 + 3i)x2 - 2x + 3ix - 2x + 4 - 6i
![Page 146: CHAPTER 2 RevIEw](https://reader031.fdocuments.net/reader031/viewer/2022020920/5681613f550346895dd0a936/html5/thumbnails/146.jpg)
Find a polynomial with the following zeros.27) 2 + 3i, 2 - 3i
(x - (2+3i))(x - (2 - 3i))(x - 2 - 3i)(x - 2 + 3i)x2 - 2x + 3ix - 2x + 4 - 6i - 3ix + 6i - 9i2
![Page 147: CHAPTER 2 RevIEw](https://reader031.fdocuments.net/reader031/viewer/2022020920/5681613f550346895dd0a936/html5/thumbnails/147.jpg)
Find a polynomial with the following zeros.27) 2 + 3i, 2 - 3i
(x - (2+3i))(x - (2 - 3i))(x - 2 - 3i)(x - 2 + 3i)x2 - 2x + 3ix - 2x + 4 - 6i - 3ix + 6i - 9i2
x2 - 2x + 3ix - 2x + 4 - 6i - 3ix + 6i - 9(-1)
![Page 148: CHAPTER 2 RevIEw](https://reader031.fdocuments.net/reader031/viewer/2022020920/5681613f550346895dd0a936/html5/thumbnails/148.jpg)
Find a polynomial with the following zeros.27) 2 + 3i, 2 - 3i
(x - (2+3i))(x - (2 - 3i))(x - 2 - 3i)(x - 2 + 3i)x2 - 2x + 3ix - 2x + 4 - 6i - 3ix + 6i - 9i2
x2 - 2x + 3ix - 2x + 4 - 6i - 3ix + 6i - 9(-1)x2 - 4x + 4 + 9
![Page 149: CHAPTER 2 RevIEw](https://reader031.fdocuments.net/reader031/viewer/2022020920/5681613f550346895dd0a936/html5/thumbnails/149.jpg)
Find a polynomial with the following zeros.27) 2 + 3i, 2 - 3i
(x - (2+3i))(x - (2 - 3i))(x - 2 - 3i)(x - 2 + 3i)x2 - 2x + 3ix - 2x + 4 - 6i - 3ix + 6i - 9i2
x2 - 2x + 3ix - 2x + 4 - 6i - 3ix + 6i - 9(-1)x2 - 4x + 4 + 9x2 - 4x + 13
![Page 150: CHAPTER 2 RevIEw](https://reader031.fdocuments.net/reader031/viewer/2022020920/5681613f550346895dd0a936/html5/thumbnails/150.jpg)
28) 0, 3, 5i, -5i
![Page 151: CHAPTER 2 RevIEw](https://reader031.fdocuments.net/reader031/viewer/2022020920/5681613f550346895dd0a936/html5/thumbnails/151.jpg)
28) 0, 3, 5i, -5i (x) (x-3) (x-5i) (x+5i)
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28) 0, 3, 5i, -5i (x) (x-3) (x-5i) (x+5i) ( x2 - 3x ) (x2 + 5ix - 5ix - 25i2 )
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28) 0, 3, 5i, -5i (x) (x-3) (x-5i) (x+5i) ( x2 - 3x ) (x2 + 5ix - 5ix - 25i2 ) ( x2 - 3x ) (x2 + 25)
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28) 0, 3, 5i, -5i (x) (x-3) (x-5i) (x+5i) ( x2 - 3x ) (x2 + 5ix - 5ix - 25i2 ) ( x2 - 3x ) (x2 + 25) x4 + 25x2 - 3x3 - 75x
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28) 0, 3, 5i, -5i (x) (x-3) (x-5i) (x+5i) ( x2 - 3x ) (x2 + 5ix - 5ix - 25i2 ) ( x2 - 3x ) (x2 + 25) x4 + 25x2 - 3x3 - 75x x4 - 3x3 + 25x2 - 75x
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Find the horizontal asymptotes, vertical asymptotes, and holes for each rational function.29)
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Find the horizontal asymptotes, vertical asymptotes, and holes for each rational function.29)
HA: y = -1
VA: x = -3
Holes: none
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Find the horizontal asymptotes, vertical asymptotes, and holes for each rational function.30)
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Find the horizontal asymptotes, vertical asymptotes, and holes for each rational function.30)
HA: y = 4
VA: x = 8
Holes: none
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Find the horizontal asymptotes, vertical asymptotes, and holes for each rational function.31)
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Find the horizontal asymptotes, vertical asymptotes, and holes for each rational function.31)
HA: y = 0
VA: x = -3, x = 6
Holes: none
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Find the horizontal asymptotes, vertical asymptotes, and holes for each rational function.32)
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Find the horizontal asymptotes, vertical asymptotes, and holes for each rational function.32)
HA: y = 0
VA: x = -1, x = 1
Holes: none
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Find the horizontal asymptotes, vertical asymptotes, and holes for each rational function.33)
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Find the horizontal asymptotes, vertical asymptotes, and holes for each rational function.33)
HA: y = 3
VA: none
Holes: none
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Find the horizontal asymptotes, vertical asymptotes, and holes for each rational function.34)
hint: this one has a hole
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Find the horizontal asymptotes, vertical asymptotes, and holes for each rational function.34)
hint: this one has a hole
HA: y = 1
VA: x = -1
Holes: x = 1
(x - 4)(x - 1)(x + 1)(x - 1)
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Find the horizontal asymptotes, vertical asymptotes, and holes for each rational function.35)
hint: this one has a hole
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Find the horizontal asymptotes, vertical asymptotes, and holes for each rational function.35)
hint: this one has a hole
HA: y = 1
VA: x = -1.5
Holes: x = 3
(2x - 1)(x - 3)(2x + 3)(x - 3)
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Year Amount, A(in hours)
2000 3492
2001 3540
2002 3606
2003 3663
2004 3757
2005 3809
36) This table shows the amounts A (in dollars) spent per person on the internet in the United States from 2000 to 2005. Use a graphing calculator to create a scatter plot of the data. Let t represent the year, with t = 0 corresponding to 2000.
a) Calculate a quadratic regression line to fit the data. What is its equation?
b) Based on your quadratic model, approximate how much was spent on each person in 2008.
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Year Amount, A(in hours)
2000 3492
2001 3540
2002 3606
2003 3663
2004 3757
2005 3809
36) This table shows the amounts A (in dollars) spent per person on the internet in the United States from 2000 to 2005. Use a graphing calculator to create a scatter plot of the data. Let t represent the year, with t = 0 corresponding to 2000.
a) Calculate a quadratic regression line to fit the data. What is its equation? f(x) = 2.36t2 + 53.7t + 3489b) Based on your quadratic model, approximate how
much was spent on each person in 2008.
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