RevIEw precalculus y x2 2 y x2 2 1 y x1 2 3 4 The number of horsepower H required to overcome wind drag on a certain car is approximated by Hs 0002s 2 005s 0029 0 lt s lt 100 ID: 308771
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Slide1
CHAPTER 2 RevIEw
precalculusSlide2Slide3
y = (x+2)
2Slide4Slide5
y = (x-2)
2
-1Slide6Slide7
y = -(x+1)
2
+ 3Slide8
4)
The number of horsepower
H
required to overcome wind drag on a certain car is approximated by
H(s) = 0.002s
2
+ 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.Slide9
4)
The number of horsepower
H
required to overcome wind drag on a certain car is approximated by
H(s) = 0.002s
2
+ 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.Slide10
4)
The number of horsepower
H
required to overcome wind drag on a certain car is approximated by
H(s) = 0.002s
2
+ 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.Slide11
4)
The number of horsepower
H
required to overcome wind drag on a certain car is approximated by
H(s) = 0.002s
2
+ 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 MPHSlide12
5) f(x) = x2 - 16
Slide13
5) f(x) = x2 -
16
= (x )(x ) Slide14
5) f(x) = x2 -
16
= (x - 4)(x + 4) Slide15
5) f(x) = x2 -
16
= (x - 4)(x + 4) zeros: 4, -4 Slide16
6) f(x) = x2 + 12x + 36Slide17
6) f(x) = x2 + 12x +
36
= (x )(x )Slide18
6) f(x) = x2 + 12x +
36
= (x + 6)(x + 6)Slide19
6) f(x) = x2 + 12x +
36
= (x + 6)(x + 6)
zeros: -6, -6Slide20
7) f(x) = 2x2 - 14x + 24 Slide21
7) f(x) = 2x2 - 14x +
24
= 2( ) Slide22
7) f(x) = 2x2 - 14x +
24
= 2(x2 - 7x + 12) Slide23
7) f(x) = 2x2 - 14x +
24
= 2(x2 - 7x + 12) = 2(x )(x )
Slide24
7) f(x) = 2x2 - 14x +
24
= 2(x2 - 7x + 12) = 2(x - 4)(x - 3)
Slide25
7) f(x) = 2x2 - 14x +
24
= 2(x2 - 7x + 12) = 2(x - 4)(x - 3)
zeros: 4, 3
Slide26
8) f(x) = x
4
- x
3 - 20x2Slide27
8) f(x) = x
4
- x
3 - 20x2
= x
2
( )Slide28
8) f(x) = x
4
- x
3 - 20x2
= x
2
(x
2 - x
- 20
x)Slide29
8) f(x) = x
4
- x
3 - 20x2
= x
2
(x
2 - x
- 20
x)
= x
2
(x )(x )
Slide30
8) f(x) = x
4
- x
3 - 20x2
= x
2
(x
2 - x
- 20
x)
= x
2
(x + 4)(x - 5)
Slide31
8) f(x) = x
4
- x
3 - 20x2
= x
2
(x
2 - x
- 20
x)
= x
2
(x + 4)(x - 5)
= (x)(x)(x + 4)(x - 5)
Slide32
8) f(x) = x
4
- x
3 - 20x2
= x
2
(x
2 - x
- 20
x)
= x
2
(x + 4)(x - 5)
= (x)(x)(x + 4)(x - 5)
zeros: 0, 0, -4, 5
Slide33
Find a polynomial with the following zeros.
9)
-7, 2
Slide34
Find a polynomial with the following zeros.
9)
-7, 2
(x - -7)(x
- 2)
Slide35
Find a polynomial with the following zeros.
9)
-7, 2
(x - -7)(x
- 2)
(
x
+ 7
)(x - 2
)
Slide36
Find a polynomial with the following zeros.
9)
-7, 2
(x - -7)(x
- 2)
(
x
+ 7
)(x - 2
)
x
2
- 2x + 7x - 14
Slide37
Find a polynomial with the following zeros.
9)
-7, 2
(x - -7)(x
- 2)
(
x
+ 7
)(x - 2
)
x
2
- 2x + 7x - 14
x
2
+ 5x -
14
Slide38
10) 0, 4Slide39
10) 0, 4
(x - 0)(x - 4)
Slide40
10) 0, 4
(x - 0)(x - 4)
x(x - 4)Slide41
10) 0, 4
(x - 0)(x - 4)
x(x - 4) x2
- 4xSlide42
What does the graph of each function look like? (circle two for each)
11)
f(x) = -x
2
+ 6x + 9
rises to the left rises to the right
falls to the left falls to the right
Slide43
What does the graph of each function look like? (circle two for each)
11)
f(x) = -x
2
+ 6x + 9
rises to the left rises to the right
falls to the left falls to the right
Slide44
What does the graph of each function look like? (circle two for each)
11)
f(x) = -x
2
+ 6x + 9
rises to the left rises to the right
falls to the left falls to the right
Slide45
12)
f(x) = 0.5x
3
+ 2x
rises to the left rises to the right
falls to the left falls to the right
Slide46
12)
f(x) = 0.5x
3
+ 2x
rises to the left rises to the right
falls to the left falls to the right
Slide47
12)
f(x) = 0.5x
3
+ 2x
rises to the left
rises to the right
falls to the left
falls to the right
Slide48
13)
f(x) = 6(x
4
+ 3x
2
+ 2)
rises to the left rises to the right
falls to the left falls to the right
Slide49
13)
f(x) = 6(x
4
+ 3x
2
+ 2)
rises to the left rises to the right
falls to the left falls to the right
Slide50
13)
f(x) = 6(x
4
+ 3x
2
+ 2)
rises to the left rises to the right
falls to the left falls to the right
Slide51
14)
f(x) = -x
5
- 7x + 10
rises to the left rises to the right
falls to the left falls to the right
Slide52
14)
f(x) = -x
5
- 7x + 10
rises to the left rises to the right
falls to the left falls to the right
Slide53
14)
f(x) = -x
5
- 7x + 10
rises to the left
rises to the right
falls to the left
falls to the right
Slide54
Use long division to simplify.
15)
(2
x
3
- 3x
2
- 50x + 75) / (2x - 3)
Slide55
Use long division to simplify.
15)
(2
x
3
- 3x
2
- 50x + 75) / (2x - 3)
2x - 3
2
x
3
- 3x
2
- 50x + 75
Slide56
Use long division to simplify.
15)
(2
x
3
- 3x
2
- 50x + 75) / (2x - 3)
x
2
2x - 3
2
x
3
- 3x
2
- 50x + 75
Slide57
Use long division to simplify.
15)
(2
x
3
- 3x
2
- 50x + 75) / (2x - 3)
x
2
2x - 3
2
x
3
- 3x
2
- 50x + 75
2
x
3
- 3x
2
Slide58
Use long division to simplify.
15)
(2
x
3
- 3x
2
- 50x + 75) / (2x - 3)
x
2
2x - 3
2
x
3
- 3x
2
- 50x + 75
2
x
3
- 3x
2
0 0
Slide59
Use long division to simplify.
15)
(2
x
3
- 3x
2
- 50x + 75) / (2x - 3)
x
2
2x - 3
2
x
3
- 3x
2
- 50x + 75
2
x
3
- 3x
2
0 0 - 50x + 75
Slide60
Use long division to simplify.
15)
(2
x
3
- 3x
2
- 50x + 75) / (2x - 3)
x
2
- 25
2x - 3
2
x
3
- 3x
2
- 50x + 75
2
x
3
- 3x
2
0 0 - 50x + 75
Slide61
Use long division to simplify.
15)
(2
x
3
- 3x
2
- 50x + 75) / (2x - 3)
x
2
- 25
2x - 3
2
x
3
- 3x
2
- 50x + 75
2
x
3
- 3x
2
0 0 - 50x + 75
- 50x + 75
Slide62
Use long division to simplify.
15)
(2
x
3
- 3x
2
- 50x + 75) / (2x - 3)
x
2
- 25
2x - 3
2
x
3
- 3x
2
- 50x + 75
2
x
3
- 3x
2
0 0 - 50x + 75
- 50x + 75
0 0
Slide63
Use long division to simplify.
15)
(2
x
3
- 3x
2
- 50x + 75) / (2x - 3)
x
2
- 25
2x - 3
2
x
3
- 3x
2
- 50x + 75
2
x
3
- 3x
2
0 0 - 50x + 75
- 50x + 75
0 0
Slide64
Use synthetic division to simplify.
16)
(3
x
3
- 17x
2
+ 15x - 25) / (x - 5)
Slide65
Use synthetic division to simplify.
16)
(3
x
3
- 17x
2
+ 15x - 25) / (x - 5)
3 -17 15 -25
Slide66
Use synthetic division to simplify.
16)
(3
x
3
- 17x
2
+ 15x - 25) / (x - 5)
5
3 -17 15 -25
Slide67
Use synthetic division to simplify.
16)
(3
x
3
- 17x
2
+ 15x - 25) / (x - 5)
5
3 -17 15 -25
3
Slide68
Use synthetic division to simplify.
16)
(3
x
3
- 17x
2
+ 15x - 25) / (x - 5)
5
3 -17 15 -25
15
3
Slide69
Use synthetic division to simplify.
16)
(3
x
3
- 17x
2
+ 15x - 25) / (x - 5)
5
3 -17 15 -25
15
3 -2
Slide70
Use synthetic division to simplify.
16)
(3
x
3
- 17x
2
+ 15x - 25) / (x - 5)
5
3 -17 15 -25
15 -10
3 -2
Slide71
Use synthetic division to simplify.
16)
(3
x
3
- 17x
2
+ 15x - 25) / (x - 5)
5
3 -17 15 -25
15 -10
3 -2 5
Slide72
Use synthetic division to simplify.
16)
(3
x
3
- 17x
2
+ 15x - 25) / (x - 5)
5
3 -17 15 -25
15 -10 25
3 -2 5
Slide73
Use synthetic division to simplify.
16)
(3
x
3
- 17x
2
+ 15x - 25) / (x - 5)
5
3 -17 15 -25
15 -10 25
3 -2 5 0
Slide74
Use synthetic division to simplify.
16)
(3
x
3
- 17x
2
+ 15x - 25) / (x - 5)
5
3 -17 15 -25
15 -10 25
3 -2 5 0
3
x
2
- 2x + 5
Slide75
17) (2x3
+ 14x
2
- 20x + 7) / (x + 6)Slide76
17) (2x3
+ 14x
2
- 20x + 7) / (x + 6) 2 14 -20 7Slide77
17) (2x3
+ 14x
2
- 20x + 7) / (x + 6) -6 2 14 -20 7Slide78
17) (2x3
+ 14x
2
- 20x + 7) / (x + 6) -6 2 14 -20 7 -12 -12 192
2 2 -32 199Slide79
17) (2x3
+ 14x
2
- 20x + 7) / (x + 6) -6 2 14 -20 7 -12 -12 192
2 2 -32 199
2x
2
+ 2x - 32 +
199
x+6Slide80
Write in completely factored form. Then find all zeros.
18)
f(x) = x3 + 4x2 - 25x - 28
Hint: (x - 4) is a
factor
Slide81
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 Slide82
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 Slide83
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 0Slide84
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
x
2
+ 8x + 7Slide85
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
x
2
+ 8x + 7
(x + 1)(x + 7)Slide86
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
x
2
+ 8x + 7
(x + 1)(x + 7)
(x - 4)(x + 1)(x + 7)Slide87
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
x
2
+ 8x + 7
(x + 1)(x + 7)
(x - 4)(x + 1)(x + 7)
zeros: 4, -1, -7Slide88
19) f(x) = x4
- 4x
3
- 7x2 + 22x + 24 Hint: (x + 2) and (x - 3) are factorsSlide89
19) f(x) = x4
- 4x
3
- 7x2 + 22x + 24 Hint: (x + 2) and (x - 3) are factors
1 -4 -7 22 24Slide90
19) f(x) = x4
- 4x
3
- 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 0Slide91
19) f(x) = x4
- 4x
3
- 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
x
3
- x
2
- 10x - 8Slide92
19) f(x) = x4
- 4x
3
- 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
x
3
- x
2
- 10x - 8
1 -1 -10 -8Slide93
19) f(x) = x4
- 4x
3
- 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
x
3
- x
2
- 10x - 8
-2 1 -1 -10 -8Slide94
19) f(x) = x4
- 4x
3
- 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
x
3
- x
2
- 10x - 8
-2 1 -1 -10 -8
-2 6 8
1 -3 -4 0Slide95
19) f(x) = x4
- 4x
3
- 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
x
3
- x
2
- 10x - 8
-2 1 -1 -10 -8
-2 6 8
1 -3 -4 0
x
2
- 3x - 4Slide96
19) f(x) = x4
- 4x
3
- 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
x
3
- x
2
- 10x - 8
-2 1 -1 -10 -8
-2 6 8
1 -3 -4 0
x
2
- 3x - 4
(x - 4)(x + 1)Slide97
19) f(x) = x4
- 4x
3
- 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
x
3
- x
2
- 10x - 8
-2 1 -1 -10 -8
-2 6 8
1 -3 -4 0
x
2
- 3x - 4
(x - 4)(x + 1)
(x - 4)(x + 1)(x + 2)(x - 3)Slide98
19) f(x) = x4
- 4x
3
- 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
x
3
- x
2
- 10x - 8
-2 1 -1 -10 -8
-2 6 8
1 -3 -4 0
x
2
- 3x - 4
(x - 4)(x + 1)
(x - 4)(x + 1)(x + 2)(x - 3) zeros: 4, -1, -2, 3Slide99
Write each complex number in standard form.
20)
(3 + 2i) + (5 +
i
)
Slide100
Write each complex number in standard form.
20)
(3 + 2i) + (5 +
i
)
8
+ 3iSlide101
21) (3 + 2i)(5 + i)
Slide102
21) (3 + 2i)(5 + i)
15 + 3i + 10i + 2i
2
Slide103
21) (3 + 2i)(5 + i)
15 + 3i + 10i + 2i
2
15 + 13i + 2i2 Slide104
21) (3 + 2i)(5 + i)
15 + 3i + 10i + 2i
2
15 + 13i + 2i2 15 + 13i + 2(-1)
Slide105
21) (3 + 2i)(5 + i)
15 + 3i + 10i + 2i
2
15 + 13i + 2i2 15 + 13i + 2(-1)
13 + 13i
Slide106
22)
(3 + 2i)
(5 +
i
)Slide107
22)
(3 + 2i)
* (5
-
i
)
(5 +
i
) * (5 -
i
)Slide108
22)
(3 + 2i)
* (5
-
i
) =
15 - 3i + 10i - 2i
2
(5 +
i
) * (5 -
i
) =
25 + 5i - 5i -
i
2Slide109
22)
(3 + 2i)
* (5
-
i
) =
15 - 3i + 10i - 2i
2
= 15 + 7i -2(-1)
(5 +
i
) * (5 -
i
) =
25 + 5i - 5i -
i
2
Slide110
22)
(3 + 2i)
* (5
-
i
) =
15 - 3i + 10i - 2i
2
=
15 + 7i -2(-1)
(5 +
i
) * (5 -
i
) =
25 + 5i - 5i -
i
2
= 25 - (-1)Slide111
22)
(3 + 2i)
* (5
-
i
) =
15 - 3i + 10i - 2i
2
=
15 + 7i -2(-1)
=
(5 +
i
) * (5 -
i
) =
25 + 5i - 5i -
i
2
= 25 - (-1)
17 + 7i
26Slide112
22)
(3 + 2i)
* (5
-
i
) =
15 - 3i + 10i - 2i
2
=
15 + 7i -2(-1)
=
(5 +
i
) * (5 -
i
) =
25 + 5i - 5i -
i
2
= 25 - (-1)
17 + 7i
26
17
+
7
i
26 26Slide113
Find all zeros. Then rewrite the function in completely factored form.
23)
f(x) = x
2
- 10x + 6
Slide114
Find all zeros. Then rewrite the function in completely factored form.
23)
f(x) = x
2
- 10x + 6
A = 1
B = -10
C = 6Slide115
Find all zeros. Then rewrite the function in completely factored form.
23)
f(x) = x
2
- 10x + 6
A = 1
B = -10
C = 6Slide116
Find all zeros. Then rewrite the function in completely factored form.
23)
f(x) = x
2
- 10x + 6
A = 1
B = -10
C = 6Slide117
Find all zeros. Then rewrite the function in completely factored form.
23)
f(x) = x
2
- 10x + 6
A = 1
B = -10
C = 6Slide118
Find all zeros. Then rewrite the function in completely factored form.
23)
f(x) = x
2
- 10x + 6
A = 1
B = -10
C = 6Slide119
Find all zeros. Then rewrite the function in completely factored form.
23)
f(x) = x
2
- 10x + 6
A = 1
B = -10
C = 6
=Slide120
Find all zeros. Then rewrite the function in completely factored form.
23)
f(x) = x
2
- 10x + 6
A = 1
B = -10
C = 6
=Slide121
24) f(x) = x2
+ 2x + 4Slide122
24) f(x) = x2
+ 2x + 4
Quadratic FormulaSlide123
24) f(x) = x2
+ 2x + 4
Quadratic Formula ---------> Magic HappensSlide124
24) f(x) = x2
+ 2x + 4
Quadratic Formula ---------> Magic Happens ------------> Slide125
24) f(x) = x2
+ 2x + 4
Quadratic Formula ---------> Magic Happens ------------> Slide126
25) f(x) = 3x4
- 4x
3
+ 7x2 + 10x - 4Slide127
25) f(x) = 3x4
- 4x
3
+ 7x2 + 10x - 4Slide128
25) f(x) = 3x4
- 4x
3
+ 7x2 + 10x - 4
-1
3 -4 7 10 -4
-3 7 -14 4
3 -7 14 -4 0
3x
3
- 7x
2
+ 14x - 4
Slide129
25) f(x) = 3x4
- 4x
3
+ 7x2 + 10x - 4
-1
3 -4 7 10 -4
-3 7 -14 4
3 -7 14 -4 0
3x
3
- 7x
2
+ 14x - 4
Slide130
25) f(x) = 3x4
- 4x
3
+ 7x2 + 10x - 4
-1
3 -4 7 10 -4
-3 7 -14 4
3 -7 14 -4 0
3x
3
- 7x
2
+ 14x - 4
3x
3
- 7x
2
+ 14x - 4Slide131
25) f(x) = 3x4
- 4x
3
+ 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
3x
3
- 7x
2
+ 14x - 4 3x
2
- 6x + 12
3x
3
- 7x
2 + 14x - 4Slide132
25) f(x) = 3x4
- 4x
3
+ 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
3x
3
- 7x
2
+ 14x - 4 3x
2
- 6x + 12
Quadratic Formula
3x3 - 7x2 + 14x - 4Slide133
25) f(x) = 3x4
- 4x
3
+ 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
3x
3
- 7x
2
+ 14x - 4 3x
2
- 6x + 12
Quadratic Formula -------> Magic Happens
3x3 - 7x2 + 14x - 4Slide134
25) f(x) = 3x4
- 4x
3
+ 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
3x
3
- 7x
2
+ 14x - 4 3x
2
- 6x + 12
Quadratic Formula -------> Magic Happens ------->
3x3 - 7x2 + 14x - 4x =x =Slide135
25) f(x) = 3x4
- 4x
3
+ 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
3x
3
- 7x
2
+ 14x - 4 3x
2
- 6x + 12
Quadratic Formula -------> Magic Happens ------->
3x3 - 7x2 + 14x - 4x =x =Slide136
26)
f(x) = x
3
- 4x
2
+ 6x - 4Slide137
26)
f(x) = x
3
- 4x
2
+ 6x - 4Slide138
26)
f(x) = x
3
- 4x
2
+ 6x - 4
2, ____, ____Slide139
26)
f(x) = x
3
- 4x
2
+ 6x - 4
2, ____, ____
Synthetic DivisionSlide140
26)
f(x) = x
3
- 4x
2
+ 6x - 4
2, ____, ____
Synthetic Division ------> x
2
- 2x + 2Slide141
26)
f(x) = x
3
- 4x
2
+ 6x - 4
2, ____, ____
Synthetic Division ------> x
2
- 2x + 2 ------> Quadratic FormulaSlide142
26)
f(x) = x
3
- 4x
2
+ 6x - 4
2,
1 +
i
, 1 -
i
Synthetic Division ------> x
2
- 2x + 2 ------> Quadratic FormulaSlide143
26)
f(x) = x
3
- 4x
2
+ 6x - 4
2,
1 +
i
, 1 -
i
(x - 2)(x - 1 -
i
)(x - 1 +
i
)
Synthetic Division ------> x
2
- 2x + 2 ------> Quadratic FormulaSlide144
Find a polynomial with the following zeros.
27)
2 + 3i, 2 - 3i
(x - (2+3i))(x - (2 - 3i))
(x - 2 - 3i)(x - 2 + 3i)
x
2
- 2x + 3ixSlide145
Find a polynomial with the following zeros.
27)
2 + 3i, 2 - 3i
(x - (2+3i))(x - (2 - 3i))
(x - 2 - 3i)(x - 2 + 3i)
x
2
- 2x + 3ix - 2x + 4 - 6iSlide146
Find a polynomial with the following zeros.
27)
2 + 3i, 2 - 3i
(x - (2+3i))(x - (2 - 3i))
(x - 2 - 3i)(x - 2 + 3i)
x
2
- 2x + 3ix - 2x + 4 - 6i - 3ix + 6i - 9i
2Slide147
Find a polynomial with the following zeros.
27)
2 + 3i, 2 - 3i
(x - (2+3i))(x - (2 - 3i))
(x - 2 - 3i)(x - 2 + 3i)
x
2
- 2x + 3ix - 2x + 4 - 6i - 3ix + 6i - 9i
2
x
2
- 2x
+ 3ix
- 2x + 4
- 6i
- 3ix
+ 6i
- 9(-1)Slide148
Find a polynomial with the following zeros.
27)
2 + 3i, 2 - 3i
(x - (2+3i))(x - (2 - 3i))
(x - 2 - 3i)(x - 2 + 3i)
x
2
- 2x + 3ix - 2x + 4 - 6i - 3ix + 6i - 9i
2
x
2
- 2x
+ 3ix
- 2x + 4
- 6i
- 3ix
+ 6i
- 9(-1)
x2 - 4x + 4 + 9Slide149
Find a polynomial with the following zeros.
27)
2 + 3i, 2 - 3i
(x - (2+3i))(x - (2 - 3i))
(x - 2 - 3i)(x - 2 + 3i)
x
2
- 2x + 3ix - 2x + 4 - 6i - 3ix + 6i - 9i
2
x
2
- 2x
+ 3ix
- 2x + 4
- 6i
- 3ix
+ 6i
- 9(-1)
x2 - 4x + 4 + 9x2 - 4x + 13Slide150
28) 0, 3, 5i, -5iSlide151
28) 0, 3, 5i, -5i (x) (x-3) (x-5i) (x+5i)Slide152
28) 0, 3, 5i, -5i (x) (x-3) (x-5i) (x+5i)
( x
2
- 3x ) (x2 + 5ix - 5ix - 25i2 )Slide153
28) 0, 3, 5i, -5i (x) (x-3) (x-5i) (x+5i)
( x
2
- 3x ) (x2 + 5ix - 5ix - 25i2 )
( x
2
- 3x ) (x
2 + 25)Slide154
28) 0, 3, 5i, -5i (x) (x-3) (x-5i) (x+5i)
( x
2
- 3x ) (x2 + 5ix - 5ix - 25i2 )
( x
2
- 3x ) (x
2 + 25) x
4
+ 25x
2
- 3x
3
- 75xSlide155
28) 0, 3, 5i, -5i (x) (x-3) (x-5i) (x+5i)
( x
2
- 3x ) (x2 + 5ix - 5ix - 25i2 )
( x
2
- 3x ) (x
2 + 25) x
4
+ 25x
2
- 3x
3
- 75x
x
4
- 3x
3
+ 25x
2
- 75xSlide156
Find the horizontal asymptotes, vertical asymptotes, and holes
for each rational function.
29)
Slide157
Find the horizontal asymptotes, vertical asymptotes, and holes
for each rational function.
29)
HA: y = -1
VA: x = -3
Holes: noneSlide158
Find the horizontal asymptotes, vertical asymptotes, and holes
for each rational function.
30)
Slide159
Find the horizontal asymptotes, vertical asymptotes, and holes
for each rational function.
30)
HA: y = 4
VA: x = 8
Holes: noneSlide160
Find the horizontal asymptotes, vertical asymptotes, and holes
for each rational function.
31)
Slide161
Find the horizontal asymptotes, vertical asymptotes, and holes
for each rational function.
31)
HA: y = 0
VA: x = -3, x = 6
Holes: noneSlide162
Find the horizontal asymptotes, vertical asymptotes, and holes
for each rational function.
32)
Slide163
Find the horizontal asymptotes, vertical asymptotes, and holes
for each rational function.
32)
HA: y = 0
VA: x = -1, x = 1
Holes: noneSlide164
Find the horizontal asymptotes, vertical asymptotes, and holes
for each rational function.
33)
Slide165
Find the horizontal asymptotes, vertical asymptotes, and holes
for each rational function.
33)
HA: y = 3
VA: none
Holes: noneSlide166
Find the horizontal asymptotes, vertical asymptotes, and holes
for each rational function.
34)
hint: this one has a holeSlide167
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)Slide168
Find the horizontal asymptotes, vertical asymptotes, and holes
for each rational function.
35)
hint: this one has a holeSlide169
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)Slide170
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.Slide171
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) = 2.36t
2
+ 53.7t + 3489
b) Based on your quadratic model, approximate how much was spent on each person in 2008.Slide172Slide173Slide174Slide175Slide176Slide177Slide178Slide179Slide180Slide181Slide182Slide183Slide184Slide185Slide186Slide187Slide188Slide189Slide190Slide191Slide192