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  1. Preface
  2. 1 Foundations
    1. Introduction
    2. 1.1 Use the Language of Algebra
    3. 1.2 Integers
    4. 1.3 Fractions
    5. 1.4 Decimals
    6. 1.5 Properties of Real Numbers
    7. Key Terms
    8. Key Concepts
    9. Exercises
      1. Review Exercises
      2. Practice Test
  3. 2 Solving Linear Equations
    1. Introduction
    2. 2.1 Use a General Strategy to Solve Linear Equations
    3. 2.2 Use a Problem Solving Strategy
    4. 2.3 Solve a Formula for a Specific Variable
    5. 2.4 Solve Mixture and Uniform Motion Applications
    6. 2.5 Solve Linear Inequalities
    7. 2.6 Solve Compound Inequalities
    8. 2.7 Solve Absolute Value Inequalities
    9. Key Terms
    10. Key Concepts
    11. Exercises
      1. Review Exercises
      2. Practice Test
  4. 3 Graphs and Functions
    1. Introduction
    2. 3.1 Graph Linear Equations in Two Variables
    3. 3.2 Slope of a Line
    4. 3.3 Find the Equation of a Line
    5. 3.4 Graph Linear Inequalities in Two Variables
    6. 3.5 Relations and Functions
    7. 3.6 Graphs of Functions
    8. Key Terms
    9. Key Concepts
    10. Exercises
      1. Review Exercises
      2. Practice Test
  5. 4 Systems of Linear Equations
    1. Introduction
    2. 4.1 Solve Systems of Linear Equations with Two Variables
    3. 4.2 Solve Applications with Systems of Equations
    4. 4.3 Solve Mixture Applications with Systems of Equations
    5. 4.4 Solve Systems of Equations with Three Variables
    6. 4.5 Solve Systems of Equations Using Matrices
    7. 4.6 Solve Systems of Equations Using Determinants
    8. 4.7 Graphing Systems of Linear Inequalities
    9. Key Terms
    10. Key Concepts
    11. Exercises
      1. Review Exercises
      2. Practice Test
  6. 5 Polynomials and Polynomial Functions
    1. Introduction
    2. 5.1 Add and Subtract Polynomials
    3. 5.2 Properties of Exponents and Scientific Notation
    4. 5.3 Multiply Polynomials
    5. 5.4 Dividing Polynomials
    6. Key Terms
    7. Key Concepts
    8. Exercises
      1. Review Exercises
      2. Practice Test
  7. 6 Factoring
    1. Introduction to Factoring
    2. 6.1 Greatest Common Factor and Factor by Grouping
    3. 6.2 Factor Trinomials
    4. 6.3 Factor Special Products
    5. 6.4 General Strategy for Factoring Polynomials
    6. 6.5 Polynomial Equations
    7. Key Terms
    8. Key Concepts
    9. Exercises
      1. Review Exercises
      2. Practice Test
  8. 7 Rational Expressions and Functions
    1. Introduction
    2. 7.1 Multiply and Divide Rational Expressions
    3. 7.2 Add and Subtract Rational Expressions
    4. 7.3 Simplify Complex Rational Expressions
    5. 7.4 Solve Rational Equations
    6. 7.5 Solve Applications with Rational Equations
    7. 7.6 Solve Rational Inequalities
    8. Key Terms
    9. Key Concepts
    10. Exercises
      1. Review Exercises
      2. Practice Test
  9. 8 Roots and Radicals
    1. Introduction
    2. 8.1 Simplify Expressions with Roots
    3. 8.2 Simplify Radical Expressions
    4. 8.3 Simplify Rational Exponents
    5. 8.4 Add, Subtract, and Multiply Radical Expressions
    6. 8.5 Divide Radical Expressions
    7. 8.6 Solve Radical Equations
    8. 8.7 Use Radicals in Functions
    9. 8.8 Use the Complex Number System
    10. Key Terms
    11. Key Concepts
    12. Exercises
      1. Review Exercises
      2. Practice Test
  10. 9 Quadratic Equations and Functions
    1. Introduction
    2. 9.1 Solve Quadratic Equations Using the Square Root Property
    3. 9.2 Solve Quadratic Equations by Completing the Square
    4. 9.3 Solve Quadratic Equations Using the Quadratic Formula
    5. 9.4 Solve Quadratic Equations in Quadratic Form
    6. 9.5 Solve Applications of Quadratic Equations
    7. 9.6 Graph Quadratic Functions Using Properties
    8. 9.7 Graph Quadratic Functions Using Transformations
    9. 9.8 Solve Quadratic Inequalities
    10. Key Terms
    11. Key Concepts
    12. Exercises
      1. Review Exercises
      2. Practice Test
  11. 10 Exponential and Logarithmic Functions
    1. Introduction
    2. 10.1 Finding Composite and Inverse Functions
    3. 10.2 Evaluate and Graph Exponential Functions
    4. 10.3 Evaluate and Graph Logarithmic Functions
    5. 10.4 Use the Properties of Logarithms
    6. 10.5 Solve Exponential and Logarithmic Equations
    7. Key Terms
    8. Key Concepts
    9. Exercises
      1. Review Exercises
      2. Practice Test
  12. 11 Conics
    1. Introduction
    2. 11.1 Distance and Midpoint Formulas; Circles
    3. 11.2 Parabolas
    4. 11.3 Ellipses
    5. 11.4 Hyperbolas
    6. 11.5 Solve Systems of Nonlinear Equations
    7. Key Terms
    8. Key Concepts
    9. Exercises
      1. Review Exercises
      2. Practice Test
  13. 12 Sequences, Series and Binomial Theorem
    1. Introduction
    2. 12.1 Sequences
    3. 12.2 Arithmetic Sequences
    4. 12.3 Geometric Sequences and Series
    5. 12.4 Binomial Theorem
    6. Key Terms
    7. Key Concepts
    8. Exercises
      1. Review Exercises
      2. Practice Test
  14. Answer Key
    1. Chapter 1
    2. Chapter 2
    3. Chapter 3
    4. Chapter 4
    5. Chapter 5
    6. Chapter 6
    7. Chapter 7
    8. Chapter 8
    9. Chapter 9
    10. Chapter 10
    11. Chapter 11
    12. Chapter 12
  15. Index

Be Prepared

9.1

8282

9.2

41054105

9.3

3x223x22

9.4

x2+18x+81x2+18x+81

9.5

y72y72

9.6

5n+425n+42

9.7

2828

9.8

6363

9.9

52i52i

9.10

y2+4y25y2+4y25

9.11

(y1)(y+1)(y1)(y+1)

9.12

x34x34; x23x23; x2x2

9.13

51,4951,49

9.14

x=23x=23

9.15

13inches13inches

9.17

x=12,x=2x=12,x=2

9.18

11

9.20

y72y72

9.21

2(x4)22(x4)2

9.22

x=32x=32

9.23

y=3,y=52y=3,y=52

9.24

,42,,42,

Try It

9.1

x=43,x=−43x=43,x=−43

9.2

y=33,y=−33y=33,y=−33

9.3

x=7,x=−7x=7,x=−7

9.4

m=4,m=−4m=4,m=−4

9.5

c=23i,c=−23ic=23i,c=−23i

9.6

c=26i,c=−26ic=26i,c=−26i

9.7

x=210,x=−210x=210,x=−210

9.8

y=27,y=−27y=27,y=−27

9.9

r=655,r=655r=655,r=655

9.10

t=833,t=833t=833,t=833

9.11

a=3+32,a=332a=3+32,a=332

9.12

b=−2+210,b=−2210b=−2+210,b=−2210

9.13

x=12+52x=12+52,x=1252x=1252

9.14

y=34+74,y=3474y=34+74,y=3474

9.15

a=5+25,a=525a=5+25,a=525

9.16

b=−3+42,b=−342b=−3+42,b=−342

9.17

r=43+22i3,r=4322i3r=43+22i3,r=4322i3

9.18

t=4+10i2,t=410i2t=4+10i2,t=410i2

9.19

m=73,m=−1m=73,m=−1

9.20

n=34,n=74n=34,n=74

9.21

(a10)2(a10)2 (b52)2(b52)2
(p+18)2(p+18)2

9.22

(b2)2(b2)2 (n+132)2(n+132)2
(q13)2(q13)2

9.23

x=−5,x=−1x=−5,x=−1

9.24

y=1,y=9y=1,y=9

9.25

y=5±10iy=5±10i

9.26

z=−4+3i,z=−43iz=−4+3i,z=−43i

9.27

x=8+43,x=843x=8+43,x=843

9.28

y=−4+33,y=−433y=−4+33,y=−433

9.29

a=−7,a=3a=−7,a=3

9.30

b=−10,b=2b=−10,b=2

9.31

p=52+612,p=52612p=52+612,p=52612

9.32

q=72+372,q=72372q=72+372,q=72372

9.33

c=−9,c=3c=−9,c=3

9.34

d=11,d=−7d=11,d=−7

9.35

m=−7,m=−1m=−7,m=−1

9.36

n=−2,n=8n=−2,n=8

9.37

r=73,r=3r=73,r=3

9.38

t=52,t=2t=52,t=2

9.39

x=38+418,x=38418x=38+418,x=38418

9.40

y=53+103,y=53103y=53+103,y=53103

9.41

y=1,y=23y=1,y=23

9.42

z=1,z=32z=1,z=32

9.43

a=−3,a=5a=−3,a=5

9.44

b=−6,b=−4b=−6,b=−4

9.45

m=−6+153,m=−6153m=−6+153,m=−6153

9.46

n=−2+265,n=−2265n=−2+265,n=−2265

9.47

a=14+314i,a=14314ia=14+314i,a=14314i

9.48

b=15+195i,b=15195ib=15+195i,b=15195i

9.49

x=−1+6,x=−16x=−1+6,x=−16

9.50

y=1+2,y=12y=1+2,y=12

9.51

c=2+73,c=273c=2+73,c=273

9.52

d=9+334,d=9334d=9+334,d=9334

9.53

r=−5r=−5

9.54

t=45t=45

9.55

2 complex solutions; 2 real solutions; 1 real solution

9.56

2 real solutions; 2 complex solutions; 1 real solution

9.57

factoring; Square Root Property; Quadratic Formula

9.58

Quadratic Forumula;
Factoring or Square Root Property Square Root Property

9.59

x=2,x=2,x=2,x=−2x=2,x=2,x=2,x=−2

9.60

x=7,x=7,x=2,x=−2x=7,x=7,x=2,x=−2

9.61

x=3,x=1x=3,x=1

9.62

y=−1,y=1y=−1,y=1

9.63

x=9,x=16x=9,x=16

9.64

x=4,x=16x=4,x=16

9.65

x=−8,x=343x=−8,x=343

9.66

x=81,x=625x=81,x=625

9.67

x=43x=2x=43x=2

9.68

x=25,x=34x=25,x=34

9.69

The two consecutive odd integers whose product is 99 are 9, 11, and −9, −11

9.70

The two consecutive even integers whose product is 128 are 12, 14 and −12, −14.

9.71

The height of the triangle is 12 inches and the base is 76 inches.

9.72

The height of the triangle is 11 feet and the base is 20 feet.

9.73

The length of the garden is approximately 18 feet and the width 11 feet.

9.74

The length of the tablecloth is approximatel 11.8 feet and the width 6.8 feet.

9.75

The length of the flag pole’s shadow is approximately 6.3 feet and the height of the flag pole is 18.9 feet.

9.76

The distance between the opposite corners is approximately 7.2 feet.

9.77

The arrow will reach 180 feet on its way up after 3 seconds and again on its way down after approximately 3.8 seconds.

9.78

The ball will reach 48 feet on its way up after approximately .6 second and again on its way down after approximately 5.4 seconds.

9.79

The speed of the jet stream was 100 mph.

9.80

The speed of the jet stream was 50 mph.

9.81

Press #1 would take 12 hours, and Press #2 would take 6 hours to do the job alone.

9.82

The red hose take 6 hours and the green hose take 3 hours alone.

9.85

up; down

9.86

down; up

9.87

x=2;x=2; (2, −7)(2, −7)

9.88

x=1;x=1; (1, −5)(1, −5)

9.89

y-intercept: (0, −8)(0, −8) x-intercepts (−4,0),(2,0)(−4,0),(2,0)

9.90

y-intercept: (0, −12)(0, −12) x-intercepts (−2,0),(6,0)(−2,0),(6,0)

9.91

y-intercept: (0, 4)(0, 4) no x-intercept

9.92

y-intercept: (0, −5)(0, −5) x-intercepts (−1, 0),(5, 0)(−1, 0),(5, 0)

9.101

The minimum value of the quadratic function is −4 and it occurs when x = 4.

9.102

The maximum value of the quadratic function is 5 and it occurs when x = 2.

9.103

It will take 4 seconds for the stone to reach its maximum height of 288 feet.

9.104

It will 6.5 seconds for the rocket to reach its maximum height of 676 feet.

9.105



This figure shows 3 upward-opening parabolas on the x y-coordinate plane. The middle graph is of f of x equals x squared has a vertex of (0, 0). Other points on the curve are located at (negative 1, 1) and (1, 1). The top curve has been moved up 1 unit, and the bottom has been moved down 1 unit.


The graph of g(x)=x2+1g(x)=x2+1 is the same as the graph of f(x)=x2f(x)=x2 but shifted up 1 unit. The graph of h(x)=x21h(x)=x21 is the same as the graph of f(x)=x2f(x)=x2 but shifted down 1 unit.

9.106



This figure shows 3 upward-opening parabolas on the x y-coordinate plane. The middle curve is the graph of f of x equals x squared and has a vertex of (0, 0). Other points on the curve are located at (negative 1, 1) and (1, 1). The top curve has been moved up 6 units, and the bottom has been moved down 6 units.


The graph of h(x)=x2+6h(x)=x2+6 is the same as the graph of f(x)=x2f(x)=x2 but shifted up 6 units. The graph of h(x)=x26h(x)=x26 is the same as the graph of f(x)=x2f(x)=x2 but shifted down 6 units.

9.109



This figure shows 3 upward-opening parabolas on the x y-coordinate plane. The middle curve is the graph of f of x equals x squared and has a vertex of (0, 0). Other points on the curve are located at (negative 1, 1) and (1, 1). The left curve has been moved to the left 2 units, and the right curve has been moved to the right 2 units.


The graph of g(x)=(x+2)2g(x)=(x+2)2 is the same as the graph of f(x)=x2f(x)=x2 but shifted left 2 units. The graph of h(x)=(x2)2h(x)=(x2)2 is the same as the graph of f(x)=x2f(x)=x2 but shift right 2 units.

9.110



This figure shows 3 upward-opening parabolas on the x y-coordinate plane. The middle curve is the graph of f of x equals x squared and has a vertex of (0, 0). Other points on the curve are located at (negative 1, 1) and (1, 1). The left curve has been moved to the left 5 units, and the right curve has been moved to the right 5 units.


The graph of g(x)=(x+5)2g(x)=(x+5)2 is the same as the graph of f(x)=x2f(x)=x2 but shifted left 5 units. The graph of h(x)=(x5)2h(x)=(x5)2 is the same as the graph of f(x)=x2f(x)=x2 but shifted right 5 units.

9.117

f(x)=−4(x+1)2+5f(x)=−4(x+1)2+5

9.118

f(x)=2(x2)25f(x)=2(x2)25

9.123


f(x)=3(x1)2+2f(x)=3(x1)2+2

The graph shown is an upward facing parabola with vertex (1, 2) and y-intercept (0, 5). The axis of symmetry is shown, x equals 1.
9.124


f(x)=−2(x2)2+1f(x)=−2(x2)2+1

The graph shown is a downward facing parabola with vertex (2, 1) and x-intercepts (1, 0) and (3, 0). The axis of symmetry is shown, x equals 2.
9.125

f(x)=(x3)24f(x)=(x3)24

9.126

f(x)=(x+3)21f(x)=(x+3)21

9.127



This figure shows an upward-opening parabola on the x y-coordinate plane. It has a vertex of (negative 2, negative 9), y-intercept of (0, 8), and axis of symmetry shown at x equals negative 2.


(−4,−2)(−4,−2)

9.128



This figure shows an upward-opening parabola on the x y-coordinate plane. It has a vertex of (4, negative 4) and x-intercepts of (2, 0) and (6, 0).


(,2][6,)(,2][6,)

9.129



A downward-facing parabola on the x y-coordinate plane. It has a vertex of (negative 3, 4), a y-intercept at (0, negative 5), and an axis of symmetry shown at x equals negative 3.


(−5,−1)(−5,−1)

9.130



A downward-facing parabola on the x y-coordinate plane. It has a vertex of (5, 9), a y-intercept at (0, negative 16), and an axis of symmetry of x equals 5.


(,2][8,)(,2][8,)

9.131

(,−4][2,)(,−4][2,)

9.132

[−3,5][−3,5]

9.133

[−12,−1+2][−12,−1+2]

9.134

(,42)(4+2,)(,42)(4+2,)

9.135

(,)(,)
no solution

9.136

no solution
(,)(,)

Section 9.1 Exercises

1.

a=±7a=±7

3.

r=±26r=±26

5.

u=±103u=±103

7.

m=±3m=±3

9.

x=±6x=±6

11.

x=±5ix=±5i

13.

x=±37ix=±37i

15.

x=±9x=±9

17.

a=±25a=±25

19.

p=±477p=±477

21.

y=±4105y=±4105

23.

u=14,u=−2u=14,u=−2

25.

m=6±25m=6±25

27.

r=12±32r=12±32

29.

y=23±229y=23±229

31.

a=7±52a=7±52

33.

x=−3±22x=−3±22

35.

c=15±335ic=15±335i

37.

x=34±72ix=34±72i

39.

m=2±22m=2±22

41.

x=3±23x=3±23

43.

x=35,x=95x=35,x=95

45.

x=76,x=116x=76,x=116

47.

r=±4r=±4

49.

a=4±27a=4±27

51.

w=1,w=53w=1,w=53

53.

a=±32a=±32

55.

p=13±73p=13±73

57.

m=±23im=±23i

59.

u=7±62u=7±62

61.

m=4±23m=4±23

63.

x=−3,x=−7x=−3,x=−7

65.

c=±566c=±566

67.

x=6±2ix=6±2i

69.

Answers will vary.

Section 9.2 Exercises

71.

(m12)2(m12)2 (x112)2(x112)2
(p16)2(p16)2

73.

(p11)2(p11)2 (y+52)2(y+52)2
(m+15)2(m+15)2

75.

u=−3,u=1u=−3,u=1

77.

x=−1,x=21x=−1,x=21

79.

m=−2±210im=−2±210i

81.

r=−3±2ir=−3±2i

83.

a=5±25a=5±25

85.

x=52±332x=52±332

87.

u=1,u=13u=1,u=13

89.

r=−2,r=6r=−2,r=6

91.

v=92±892v=92±892

93.

x=5±30x=5±30

95.

x=−7,x=3x=−7,x=3

97.

x=−5,x=−1x=−5,x=−1

99.

m=−11,m=1m=−11,m=1

101.

n=1±14n=1±14

103.

c=−2,c=32c=−2,c=32

105.

x=−5,x=32x=−5,x=32

107.

p=74±1614p=74±1614

109.

x=310±19110ix=310±19110i

111.

Answers will vary.

Section 9.3 Exercises

113.

m=−1,m=34m=−1,m=34

115.

p=12,p=3p=12,p=3

117.

p=−4,p=−3p=−4,p=−3

119.

r=−3,r=11r=−3,r=11

121.

u=−7±736u=−7±736

123.

a=3±32a=3±32

125.

x=−4±25x=−4±25

127.

y=−2,y=13y=−2,y=13

129.

x=34±154ix=34±154i

131.

x=38±78ix=38±78i

133.

v=2±13v=2±13

135.

y=3±1932y=3±1932

137.

m=−1,m=34m=−1,m=34

139.

b=−2±226b=−2±226

141.

c=34c=34

143.

q=35q=35

145.

no real solutionsno real solutions 11
22

147.

11 no real solutionsno real solutions
22

149.


factorfactor
square rootsquare root
Quadratic FormulaQuadratic Formula

151.


Quadratic FormulaQuadratic Formula
square rootsquare root
factorfactor

153.

Answers will vary.

Section 9.4 Exercises

155.

x=±3,x=±2x=±3,x=±2

157.

x=±15,x=±2ix=±15,x=±2i

159.

x=±1,x=±62x=±1,x=±62

161.

x=±3,x=±22x=±3,x=±22

163.

x=−1,x=12x=−1,x=12

165.

x=53,x=0x=53,x=0

167.

x=0,x=±3x=0,x=±3

169.

x=±222,x=±7x=±222,x=±7

171.

x=25x=25

173.

x=4x=4

175.

x=14x=14

177.

x=125, x=94 x=125,x=94

179.

x=−1,x=−512x=−1,x=−512

181.

x=8,x=−216x=8,x=−216

183.

x=278,x=6427x=278,x=6427

185.

x=27512,x=125x=27512,x=125

187.

x=1,x=49x=1,x=49

189.

x=−2,x=35x=−2,x=35

191.

x=−2,x=43x=−2,x=43

193.

Answers will vary.

Section 9.5 Exercises

195.

Two consecutive odd numbers whose product is 255 are 15 and 17, and −15 and −17.

197.

The first and second consecutive odd numbers are 24 and 26, and −26 and −24.

199.

Two consecutive odd numbers whose product is 483 are 21 and 23, and −21 and −23.

201.

The width of the triangle is 5 inches and the height is 18 inches.

203.

The base is 24 feet and the height of the triangle is 10 feet.

205.

The length of the driveway is 15.0 feet and the width is 3.3 feet.

207.

The length of table is 8 feet and the width is 3 feet.

209.

The lengths of the three sides of the triangle are 1.7, 3, and 3.5 ft.

211.

The length of the diagonal fencing is 7.3 yards.

213.

The ladder will reach 24.5 feet on the side of the house.

215.

The rocket will reach 1200 feet on its way up at 1.97 seconds and on its way down at 38.03 seconds.

217.

The bullet will take 70 seconds to hit the ground.

219.

The speed of the wind was 49 mph.

221.

The speed of the current was 4.3 mph.

223.

The less experienced painter takes 6 hours and the experienced painter takes 3 hours to do the job alone.

225.

Machine #1 takes 3.6 hours and Machine #2 takes 4.6 hours to do the job alone.

227.

Answers will vary.

Section 9.6 Exercises

229.
This figure shows an upward-opening parabola graphed on the x y-coordinate plane. The x-axis of the plane runs from negative 10 to 10. The y-axis of the plane runs from negative 10 to 10. The parabola has a vertex at (0, 3).
231.
This figure shows a downward-opening parabola graphed on the x y-coordinate plane. The x-axis of the plane runs from negative 10 to 10. The y-axis of the plane runs from negative 10 to 10. The parabola has a vertex at (0, 1).
233.

down up

235.

down up

237.

x=−4x=−4; (−4, −17)(−4, −17)

239.

x=1x=1; (1,6)(1,6)

241.

y-intercept: (0, 6);(0, 6); x-intercept (−1, 0),(−6, 0)(−1, 0),(−6, 0)

243.

y-intercept: (0, 12);(0, 12); x-intercept (−2, 0),(−6, 0)(−2, 0),(−6, 0)

245.

y-intercept: (0, −19);(0, −19); x-intercept: none

247.

y-intercept: (0, 13);(0, 13); x-intercept: none

249.

y-intercept: (0,25);(0,25); x-intercept (52,0)(52,0)

251.

y-intercept: (0,−9);(0,−9); x-intercept (−3, 0)(−3, 0)

253.
This figure shows an upward-opening parabola graphed on the x y-coordinate plane. The x-axis of the plane runs from negative 10 to 10. The y-axis of the plane runs from negative 10 to 10. The parabola has a vertex at (negative 3, negative 4). The y-intercept, point (0, 5), is plotted as are the x-intercepts, (negative 5, 0) and (negative 1, 0).
255.
This figure shows an upward-opening parabola graphed on the x y-coordinate plane. The x-axis of the plane runs from negative 10 to 10. The y-axis of the plane runs from negative 10 to 10. The parabola has a vertex at (negative 2, negative 1). The y-intercept, point (0, 3), is plotted as are the x-intercepts, (negative 3, 0) and (negative 1, 0).
257.
This figure shows an upward-opening parabola graphed on the x y-coordinate plane. The x-axis of the plane runs from negative 4 to 4. The y-axis of the plane runs from negative 4 to 4. The parabola has a vertex at (negative 2 thirds, 0). The y-intercept, point (0, 4), is plotted. The axis of symmetry, x equals negative 2 thirds, is plotted as a dashed vertical line.
259.
This figure shows a downward-opening parabola graphed on the x y-coordinate plane. The x-axis of the plane runs from negative 10 to 10. The y-axis of the plane runs from negative 15 to 10. The parabola has a vertex at (1, negative 6). The y-intercept, point (0, negative 7), is plotted. The axis of symmetry, x equals 1, is plotted as a dashed vertical line.
261.
This figure shows an upward-opening parabola graphed on the x y-coordinate plane. The x-axis of the plane runs from negative 10 to 10. The y-axis of the plane runs from negative 10 to 10. The parabola has a vertex at (1, negative 1). The y-intercept, point (0, 1), is plotted as are the x-intercepts, approximately (0.3, 0) and (1.7, 0). The axis of symmetry is the vertical line x equals 1, plotted as a dashed line.
263.
This figure shows an upward-opening parabola graphed on the x y-coordinate plane. The x-axis of the plane runs from negative 10 to 10. The y-axis of the plane runs from negative 10 to 10. The parabola has a vertex at (1, 0). This point is the only x-intercept. The y-intercept, point (0, 2), is plotted. The axis of symmetry is the vertical line x equals 1, plotted as a dashed line.
265.
This figure shows a downward-opening parabola graphed on the x y-coordinate plane. The x-axis of the plane runs from negative 10 to 10. The y-axis of the plane runs from negative 10 to 10. The parabola has a vertex at (negative 2, 6). The y-intercept, point (0, 2), is plotted as are the x-intercepts, approximately (negative 4.4, 0) and (0.4, 0). The axis of symmetry is the vertical line x equals 2, plotted as a dashed line.
267.
This figure shows an upward-opening parabola graphed on the x y-coordinate plane. The x-axis of the plane runs from negative 10 to 10. The y-axis of the plane runs from negative 10 to 10. The parabola has a vertex at (1, 3). The y-intercept, point (0, 8), is plotted; there are no x-intercepts. The axis of symmetry is the vertical line x equals 1, plotted as a dashed line.
269.
This figure shows an upward-opening parabola graphed on the x y-coordinate plane. The x-axis of the plane runs from negative 10 to 10. The y-axis of the plane runs from negative 10 to 10. The parabola has a vertex at (negative 3, negative 7). The x-intercepts are plotted at the approximate points (negative 4.5, 0) and (negative 1.5, 0). The axis of symmetry is the vertical line x equals negative 3, plotted as a dashed line.
271.

The minimum value is 9898 when x=14.x=14.

273.

The minimum value is 6 when x = 3.

275.

The maximum value is 16 when x = 0.

277.

In 5.3 sec the arrow will reach maximum height of 486 ft.

279.

In 3.4 seconds the ball will reach its maximum height of 185.6 feet.

281.

A selling price of $20 per computer will give the maximum revenue of $400.

283.

A selling price of $35 per pair of boots will give a maximum revenue of $1,225.

285.

The length of one side along the river is 120 feet and the maximum are is 7,200 square feet.

287.

The maximum area of the patio is 800 feet.

289.

Answers will vary.

291.

Answers will vary.

Section 9.7 Exercises

293.



This figure shows 3 upward-opening parabolas on the x y-coordinate plane. The middle curve is the graph of f of x equals x squared and has a vertex of (0, 0). Other points on the curve are located at (negative 1, 1) and (1, 1). The top curve has been moved up 4 units, and the bottom has been moved down 4 units.


The graph of g(x)=x2+4g(x)=x2+4 is the same as the graph of f(x)=x2f(x)=x2 but shifted up 4 units. The graph of h(x)=x24h(x)=x24 is the same as the graph of f(x)=x2f(x)=x2 but shift down 4 units.

295.
This figure shows an upward-opening parabolas on the x y-coordinate plane. It has a vertex of (0, 3) and other points (7, 2) and (7, negative 2).
297.
This figure shows an upward-opening parabolas on the x y-coordinate plane. It has a vertex of (0, 2) and other points (negative 2, 6) and (2, 6).
299.
This figure shows an upward-opening parabolas on the x y-coordinate plane. It has a vertex of (0, negative 4) and other points (negative 2, 0) and (2, 0).
301.



This figure shows 3 upward-opening parabolas on the x y-coordinate plane. One is the graph of f of x equals x squared and has a vertex of (0, 0). Other points on the curve are located at (negative 1, 1) and (1, 1). The graph to the right is shifted 3 units to the right to produce g of x equals the quantity of x minus 3 squared. The graph the left is shifted 3 units to the left to produce h of x equals the quantity of x plus 3 squared.


The graph of g(x)=(x3)2g(x)=(x3)2 is the same as the graph of f(x)=x2f(x)=x2 but shifted right 3 units. The graph of h(x)=(x+3)2h(x)=(x+3)2 is the same as the graph of f(x)=x2f(x)=x2 but shifted left 3 units.

303.


This figure shows an upward-opening parabolas on the x y-coordinate plane. It has a vertex of (2, 0) and other points (0, 4) and (4, 4).
305.


This figure shows an upward-opening parabolas on the x y-coordinate plane. It has a vertex of (negative 5, 0) and other points (negative 7, 4) and (negative 3, 4).
307.


This figure shows an upward-opening parabolas on the x y-coordinate plane. It has a vertex of (5, 0) and other points (3, 4) and (7, 4).
309.


This figure shows an upward-opening parabolas on the x y-coordinate plane. It has a vertex of (negative 2, 1) and other points (negative 4, 5) and (0, 5).
311.


This figure shows an upward-opening parabolas on the x y-coordinate plane. It has a vertex of (1, 5) and other points (negative 1, 9) and (3, 9).
313.


This figure shows an upward-opening parabolas on the x y-coordinate plane. It has a vertex of (negative 3, 1) and other points (negative 4, 0) and (negative 2, 0).
315.


This figure shows an upward-opening parabolas on the x y-coordinate plane. It has a vertex of (4, negative 2) and other points (3, negative 2) and (5, negative 2).
317.


This figure shows a downward-opening parabolas on the x y-coordinate plane. It has a vertex of (0, 0) and other points (negative 1, negative 2) and (1, negative 2).
319.


This figure shows a downward-opening parabolas on the x y-coordinate plane. It has a vertex of (0, 0) and other points (negative 1, negative 4) and (1, negative 4).
321.


This figure shows an upward-opening parabolas on the x y-coordinate plane. It has a vertex of (0, 0) and other points (negative 2, 2) and (2, 2).
323.


This figure shows an upward-opening parabolas on the x y-coordinate plane. It has a vertex of (0, 0) and other points (2, 1) and (negative 2, 1).
325.

f(x)=−3(x+2)2+7f(x)=−3(x+2)2+7

327.

f(x)=3(x+1)24f(x)=3(x+1)24

329.

f(x)=(x+3)24f(x)=(x+3)24

This figure shows an upward-opening parabolas on the x y-coordinate plane. It has a vertex of (negative 3, 3), y-intercept of (0, 5), and axis of symmetry shown at x equals negative 3.
331.

f(x)=(x+2)21f(x)=(x+2)21

This figure shows an upward-opening parabolas on the x y-coordinate plane. It has a vertex of (negative 2, negative 1), y-intercept of (0, 3), and axis of symmetry shown at x equals negative 2.
333.

f(x)=(x3)2+6f(x)=(x3)2+6

This figure shows an upward-opening parabolas on the x y-coordinate plane. It has a vertex of (3, 6), y-intercept of (0, 10), and axis of symmetry shown at x equals 3.
335.

f(x)=(x4)2+0f(x)=(x4)2+0

This figure shows a downward-opening parabola on the x y-coordinate plane. It has a vertex of (4, 0), y-intercept of (0, negative 16), and axis of symmetry shown at x equals 4.
337.

f(x)=(x+2)2+6f(x)=(x+2)2+6

This figure shows a downward-opening parabola on the x y-coordinate plane. It has a vertex of (negative 2, 6), y-intercept of (0, 2), and axis of symmetry shown at x equals negative 2.
339.

f(x)=5(x1)2+3f(x)=5(x1)2+3

This figure shows an upward-opening parabola on the x y-coordinate plane. It has a vertex of (1, 3), y-intercept of (0, 8), and axis of symmetry shown at x equals 1.
341.

f(x)=2(x1)21f(x)=2(x1)21

This figure shows an upward-opening parabola on the x y-coordinate plane. It has a vertex of (1, negative 1), y-intercept of (0, 1), and axis of symmetry shown at x equals 1.
343.

f(x)=−2(x2)22f(x)=−2(x2)22

This figure shows a downward-opening parabola on the x y-coordinate plane. It has a vertex of (2, negative 2), y-intercept of (0, negative 10), and axis of symmetry shown at x equals 2.
345.

f(x)=2(x+1)2+4f(x)=2(x+1)2+4

This figure shows an upward-opening parabola on the x y-coordinate plane. It has a vertex of (negative 1, 4), y-intercept of (0, 6), and axis of symmetry shown at x equals negative 1.
347.

f(x)=(x1)23f(x)=(x1)23

This figure shows a downward-opening parabola on the x y-coordinate plane. It has a vertex of (1, negative 3), y-intercept of (0, negative 4), and axis of symmetry shown at x equals 1.
349.

351.

353.

355.

357.

f(x)=(x+1)25f(x)=(x+1)25

359.

f(x)=2(x1)23f(x)=2(x1)23

361.

Answers will vary.

Section 9.8 Exercises

363.



The graph shown is an upward-facing parabola with vertex (negative 3, negative 4) and y-intercept (0,5).


(,−5)(−1,)(,−5)(−1,)

365.



The graph shown is an upward facing parabola with vertex (negative 2, negative 1) and y-intercept (0,3).


[−3,−1][−3,−1]

367.



The graph shown is a downward-facing parabola with vertex (negative 1 and 5 tenths, 20) and y-intercept (0, 18).


(,−6][3,)(,−6][3,)

369.



The graph shown is a downward facing parabola with a y-intercept of (0, 12) and x-intercepts (negative 3, 0) and (4, 0).


[−3,4][−3,4]

371.

(,−4][1,)(,−4][1,)

373.

(2,5)(2,5)

375.

(,−5)(−3,)(,−5)(−3,)

377.

[22,2+2][22,2+2]

379.

(,56)(5+6,)(,56)(5+6,)

381.

23,5223,52

383.

[12,4][12,4]

385.

(,).(,).

387.

no solution

389.

(,).(,).

391.

Answers will vary.

393.

Answers will vary.

Review Exercises

395.

y=±12y=±12

397.

a=±5a=±5

399.

r=±42ir=±42i

401.

w=±53w=±53

403.

p=1,p=9p=1,p=9

405.

x=14±34x=14±34

407.

n=4±102n=4±102

409.

n=−5±23n=−5±23

411.

(x+11)2(x+11)2

413.

(a32)2(a32)2

415.

d=−13,−1d=−13,−1

417.

m=−3±10im=−3±10i

419.

v=7±32v=7±32

421.

m=−9,−1m=−9,−1

423.

a=32±412a=32±412

425.

u=−6±32u=−6±32

427.

p=0,6p=0,6

429.

y=12,2y=12,2

431.

c=13±273c=13±273

433.

x=32±12ix=32±12i

435.

x=14,1x=14,1

437.

r=−6,7r=−6,7

439.

v=54,1v=54,1

441.

m=−4±103m=−4±103

443.

a=512±2312ia=512±2312i

445.

u=5±22u=5±22

447.

p=4±65p=4±65

449.

c=12c=12

451.

1 2 2 0

453.

factor Quadratic Formula square root

455.

x=±2,±23x=±2,±23

457.

x=±1,±12x=±1,±12

459.

x=16x=16

461.

x=64,216x=64,216

463.

x=−2,43x=−2,43

465.

Two consecutive even numbers whose product is 624 are 24 and 26, and −24 and −26.

467.

The height is 14 inches and the width is 10 inches.

469.

The length of the diagonal is 3.6 feet.

471.

The width of the serving table is 4.7 feet and the length is 16.1 feet.

Four tables arranged end-to-end are shown. Together, they have an area of 75 feet. The short side measures w and the long side measures 3 times w plus 2.
473.

The speed of the wind was 30 mph.

475.

One man takes 3 hours and the other man 6 hours to finish the repair alone.

477.


This figure shows a downward-opening parabola on the x y-coordinate plane. It has a vertex of (3, 0) and other points of (negative 2, negative 1) and (2, negative 1).
479.

up down

481.

x=2;(2,−7)x=2;(2,−7)

483.

y:(0,15)x:(3,0),(5,0)y:(0,15)x:(3,0),(5,0)

485.

y:(0,−46)x:noney:(0,−46)x:none

487.

y:(0,64)x:(−8,0)y:(0,64)x:(−8,0)

489.


This figure shows an upward-opening parabola on the x y-coordinate plane. It has a vertex of (1, negative 4) and a y-intercept of (0, negative 3).
491.


This figure shows an upward-opening parabola on the x y-coordinate plane. It has a vertex of (one-half, 0) and a y-intercept of (0, 1).
493.


This figure shows a downward-opening parabola on the x y-coordinate plane. It has a vertex of (negative 2, negative 4) and a y-intercept of (0, negative 12).
495.

The maximum value is 2 when x = 2.

497.

The length adjacent to the building is 90 feet giving a maximum area of 4,050 square feet.

499.


This figure shows an upward-opening parabola on the x y-coordinate plane. It has a vertex of (negative 3, 0) and other points of (negative 1, negative 2) and (1, negative 2).
501.


This figure shows an upward-opening parabola on the x y-coordinate plane. It has a vertex of (3, 0) and other points of (2, 1) and (4,1).
503.


This figure shows an upward-opening parabola on the x y-coordinate plane. It has a vertex of (negative 3, negative 2) and other points of (negative 5, 2) and (negative 1, 2).
505.


This figure shows an upward-opening parabola on the x y-coordinate plane. It has a vertex of (4, negative 3) and other points of (3, negative 2) and (5, negative 2).
507.


This figure shows a downward-opening parabola on the x y-coordinate plane. It has a vertex of (0, 0) and other points of (negative 1, negative 1) and (1, negative 1).
509.

f(x)=2(x1)26f(x)=2(x1)26

511.

f(x)=3(x1)24f(x)=3(x1)24

This figure shows an upward-opening parabola on the x y-coordinate plane. It has a vertex of (1, negative 4) and other points of (0, negative 1) and (2, negative 1).
513.

f(x)=2(x+1)2+4f(x)=2(x+1)2+4

This figure shows an upward-opening parabola on the x y-coordinate plane. It has a vertex of (negative 1, 4) and other points of (negative 2, 6) and (0, 6).
515.

f(x)=−3(x+2)2+7f(x)=−3(x+2)2+7

This figure shows a downward-opening parabola on the x y-coordinate plane. It has a vertex of (negative 2, 7) and other points of (negative 4, negative 5) and (0, negative 5).
517.

f(x)=(x+1)25f(x)=(x+1)25

519.



This figure shows an upward-opening parabola on the x y-coordinate plane. It has a vertex of (one-half, negative 6 and one-fourth) and other points of (0, negative 6) and (1, negative 6).


(,−2)(3,)(,−2)(3,)

521.



This figure shows a downward-opening parabola on the x y-coordinate plane. It has a vertex of (negative one-half, 2 and one-fourth) and other points of (negative 2, 0) and (1, 0).


[−2,1][−2,1]

523.

(2,4)(2,4)

525.

[35,3+5][35,3+5]

527.

no solution

Practice Test

529.

w=−2,w=−8w=−2,w=−8

531.

m=1,m=32m=1,m=32

533.

y=23y=23

535.

2 complex

537.

y=1,y=−27y=1,y=−27

539.

down x=−4x=−4
(−4,0)(−4,0) y:(0,−16);x:(−4,0)y:(0,−16);x:(−4,0)
maximum value of 00 when x=−4x=−4

541.
This figure shows a downward-opening parabola on the x y-coordinate plane. It has a vertex of (2, 12) and other points of (0, 4) and (4, 4).
543.


This figure shows an upward-opening parabola on the x y-coordinate plane. It has a vertex of (2, negative 5) and other points of (0, negative 1) and (4, negative 1).


f(x)=2(x1)26f(x)=2(x1)26

545.

(,52)(2,)(,52)(2,)

547.

The diagonal is 4.4 units long.

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