answers - mrshallalgebra2.files.wordpress.com · 2 5 followed by a translation 3 units right of the...

Answers

Copyright © Big Ideas Learning, LLC Algebra 2 All rights reserved. Answers

A1

Chapter 1

1.1 Start Thinking

As the string V gets wider, the points on the string

move closer to the x-axis. This activity mimics a

vertical shrink of a parabola.

1.1 Warm Up

1. 2.

3. 4.

1.1 Cumulative Review Warm Up

1. 12

2. 1 3. 12

4. 25

1.1 Practice A

1. quadratic; The graph of f is a vertical shrink by a

factor of 13

followed by a translation 1 unit down

of the graph of the parent quadratic function.

2. constant; The graph of f is a translation 1 unit up of

the graph of the parent constant function.

3. a linear function

4.

Sample answer: The graph of h is a translation

2 units up of the graph of the parent linear function.

5.

Sample answer: The graph of f is a translation

3 units right of the parent linear function.

6.

The graph of g is a translation 2 units up of the

parent quadratic function.

7.

The graph of f is a translation 1 unit right of the

graph of the parent quadratic function.

8.

The graph of h is a translation 4 units left of the

graph of the parent function.

9.

The graph of f is a translation 4 units up of the

graph of the parent constant function.

Answers

Algebra 2 Copyright © Big Ideas Learning, LLC Answers All rights reserved. A2

10.

Sample answer: The graph of f is a vertical stretch

by a factor of 3 of the graph of the parent linear

function.

11.

Sample answer: The graph of g is a vertical shrink

by a factor of 12

of the parent linear function.

12.

The graph of h is a vertical stretch by a factor of

3 of the graph of the parent quadratic function.

13.

Sample answer: The graph of g is a vertical shrink

by a factor of 14

of the graph of the parent quadratic

function.

14.


2 of the graph of the parent absolute value function.

15.

Sample answer: The graph of f is a vertical stretch

by a factor of 52

of the graph of the parent linear

function.

16.

The graph of f is a vertical shrink by a factor of 13

followed by a translation 1 unit down of the graph


17.


2 followed by a translation 3 units down of the

graph of the parent absolute value function.

Answers


A3

18.

The graph of g is a vertical stretch by a factor of 53

followed by a translation 2 units up of the graph of

the parent quadratic function.

19. Sample answer:

The graph of g is a translation 3 units up of the


1.1 Practice B

1. absolute value; The graph of f is a vertical shrink by

a factor of 25

followed by a translation 3 units right

of the graph of the parent absolute value function.

2. linear; The graph of f is a vertical stretch by a factor

of 2 followed by a translation 1 unit up of the graph


3.

Sample answer: The graph of h is a translation

2 units up of the graph of the parent linear function.

4.

Sample answer: The graph of f is a reflection in the

x-axis of the graph of the parent linear function.

5.

The graph of g is a reflection in the x-axis of the


6.

The graph of f is a translation 2 units left of the


7.

The graph of h is a translation 2 units down of the


8.

The graph of f is a translation 4 units down of the

parent constant function.

Answers


9.

Sample answer: The graph of f is a vertical shrink

by a factor of 35

of the graph of the parent linear

function.

10.

Sample answer: The graph of h is a vertical stretch

by a factor of 32

of the graph of the parent absolute

value function.

11.

The graph of h is a vertical stretch by a factor of 43

of the graph of the parent quadratic function.

12.

The graph of g is a vertical shrink by a factor of 110

followed by a translation 5 units up of the graph of


13.

The graph of h is a translation 5 units right and 49

units up of the graph of the parent quadratic

function.

14.

The graph of f is a reflection in the x-axis, followed

by a translation 2 units left and 13

units down of the


15. absolute value; domain: all real numbers, range:

3y

16. linear; domain: all real numbers, range: all real

numbers

17. quadratic; domain: all real numbers, range:

3y

18. a. quadratic function

b. 0; t is the number of seconds after the ball is

thrown, so when the ball is thrown 0.t

c. 6 ft; 0 6f

1.1 Enrichment and Extension

1.

Sample answer: Trapezoid A B C D a reflection in

the x-axis, followed by translation 1 unit down and

6 units left of trapezoid ABCD.

Answers


A5

1.1 Puzzle Time

BECAUSE PEOPLE ALWAYS SAY IF IT IS NOT

BROKEN DO NOT FIX IT

1.2 Practice A

9. 4 12g x x 10. 43

1g x x

11. 9 2g x x 12. 13

1g x x

13. 13

4g x x 14. 2 3g x x

1.2 Practice B

13. 514 4

g x x 14. 2g x x

Answers


5. 0.42 2.67; 0.65;y x r The points lie

somewhat close to the line.

6. 6; 0.85;y x r The points lie close to

the line.


1. 4y 2. 23

2y x 3. 7y

4. 12

3y x 5. 9 6. 14

7. 32

8. 18 9. 3 10. 43

11. 54

2488; $30,750y x

12. 74

3490; $36,250; $5500y x

1.3 Puzzle Time

ROADTRIP

1.4 Start Thinking

The point of intersection of the three models would be

when all three models create the same profit for the

same cost.

1.4 Warm Up

1. 3 32 2

y x 2. 713 2

y x

3. 32

y x 4. 7 132 2

y x

5. 514 4

y x 6. 7 198 8

y x


1. yes 2. no 3. no

4. yes 5. no 6. yes

1.4 Practice A

1. 1, 3, 7 2. 2, 1, 5

3. Each term of the second equation should be

multiplied by 5.

5 3 15

5 10 15 50

13 14 65

x y z

x y z

y z

4. no solution

5. Any ordered triple of the form , 0, 2x x is a

solution of the system.

6. Roses cost $3 each, carnations cost $1 each, and

tulips cost $3 each.

7. 4, 3, 4 8. 7, 2, 1

9. a.

54

90

5 5

m n

m n

m n

41, 40, 9m n

b. yes; 2 2 29 40 41

1.4 Practice B

1. 1, 1, 3 2. 2, 1, 4

3. Each term of the first equation should be multiplied

by 3.

15 9 3 45

3 4 3 8

18 5 53

x y z

x y z

x y

4. no solution

5. Any ordered triple of the form , 2 2 , 1x x x

is a solution.

6. 5, 4, 3 7. no solution

8. no; The solution of the system is 16.4 nickels,

8.2 dimes, and 5.4 quarters. You cannot have part

of a coin.

9. a. 715 5,

b. yes; There is one solution, so the lines intersect

at a point.

Answers


A7


1. 3, 2, 2, 1 2. 0, 3, 1, 4 3. 5, 2, 3, 4

1.4 Puzzle Time

THE TALLEST LIVING HORSE WHO MEASURED

SIX FEET TEN INCHES

Cumulative Review

1. solution 2. solution

3. not a solution 4. solution




11. solution 12. solution

13. 10.5 12t

14. a. 21 25m b. 1.5 gal c. 4 gal

15. 1z 16. 4c 17. 6y

18. 10h 19. 9p 20. 49b

21. 18

r 22. 7s

23. 5 and 13f f 24. 253

3 and k k

25. 9 52 2 and g g 26. 3 5

4 4 and v v

27. 1 and 9w w 28. 13 and 1d d

29. 3 2y x 30. 9 8y x

31. 2 1y x 32. 512 2

y x

33. 6 12y x 34. 5 30y x

35. 543 3

y x 36. 2 8y x

37. 7 7 1

or 5 5 5

xy y

x x

38. 108

x 39. 55 x

40. 32 x 41. 40x

42. a. 2.50 2.25m b. $22.75 c. $27.25 d. $34.75

43. a. 2.12p b. $10.60 c. $7.28

d. 9.43 lbs, or about 9 lbs

44. 26 min 45. 3 gigabytes

46. Distributive Property

47. Additive Inverse Property

48. Commutative Property of Multiplication

49. Associative Property of Multiplication

50. Commutative Property of Addition

51. Associative Property of Addition

52. Additive Identity Property

53. Multiplicative Identity Property

54.

55.

56. 57.

Answers


58. 7, 3 59. 4, 9 60. 1, 7

61. no solution 62. 2, 7 63. no solution

64. no solution 65. 7, 2

66. infinitely many solutions

67. 1, 7


69. 2, 9 70. 29 12 4a a

71. 2 14 49b b 72. 225 90 81c c

73. 29 48 64d d 74. 216 32 16m m

75. 24 4 1n n 76. 225 60 36p p

77. 2 4 4q q

78. x-intercept: 3, y-intercept: 2




3



84. 2 3y x 85. 4y x

86. 14

1y x 87. 34

5y x

88. 4y x 89. 45

y

90. 2 17 2

y x 91. 23

2y x

92. 2 3g x x 93. 5 5g x x

94. 3 2 15g x x

95. 2 6g x x


97. 2, 4, 7


99. no solution 100. 3, 4, 2

101. 1, 4, 7 102. 3 in. by 6 in.

103. a. You need 7.5 pounds of peanuts, 3.5 pounds

of raisins, 4.5 pounds of pretzels, and 3 pounds

of chocolate candy pieces.

b. Recipe B c. 3 lbs

104. your friend; $6.50

Chapter 2

2.1 Start Thinking

Sample answer:

2( )f x x

2( ) ( 1)f x x

2( ) 2f x x

2( ) 1f x x

The function 2( ) ( 1)f x x is a horizontal

translation 1 unit right ( 1).h The function

2( ) 2f x x is a vertical stretch by a factor of 2

( 2).a The function 2( ) 1f x x is a vertical

translation 1 unit up ( 1).k

x −2 −1 0 1 2

( )f x 4 1 0 1 4

x −2 −1 0 1 2

( )f x 9 4 1 0 1

x −2 −1 0 1 2

( )f x 8 2 0 2 8

x −2 −1 0 1 2

( )f x 5 2 1 2 5

Answers


A9

2.1 Warm Up

1. 26 16 8x x 2. 220 13 2x x

3. 2 28 10 3x xy y 4. 212 3a a

5. 220 3 2x x 6. 215 22 8y y


1. ( ) 3g x x 2. ( ) 2g x x

3. ( ) 5 2 4g x x

2.1 Practice A

1. The graph of g is a translation 2 units down of the

graph of f.

2. The graph of g is a translation 1 unit up of the

graph of f.

3. The graph of g is a translation 1 unit left of the

graph of f.

4. The graph of g is a translation 2 units right of the

graph of f.

5. The graph of g is a translation 5 units right of the

graph of f.

6. The graph of g is a translation 2 units left and 1 unit

down of the graph of f.

7. The graph of g is a reflection in the x-axis followed

by a vertical stretch by a factor of 2 of the graph

of f.

8. The graph of g is a reflection in the y-axis followed

by a horizontal shrink of the graph of f by a factor

of 12.

9. The graph of g is a

vertical shrink by a

factor of 14

of the

graph of f.

Answers


10. When 0 1a in the function ( ) ( ),g x a f x

the transformation is a vertical shrink, not stretch;

The graph of g is a reflection in the x-axis followed

by a vertical shrink by a factor of 13

of the graph of


11. The graph is a vertical stretch by a factor of 2,

followed by a translation 3 units left and 2 units up

of the parent quadratic function; ( 3, 2)

12. The graph is a reflection in the x-axis, followed by

a vertical stretch by a factor of 5 and a translation

1 unit down of the parent quadratic function;

(0, 1)

13. 2( ) 3 3; (0, 3)g x x

14. 2( ) 7; (0, 7)g x x

15. a. 22, 3, 4; ( ) (2 3) 4a h k g x x

b. 24, 3, 4; ( ) 4( 3) 4a h k g x x

2.1 Practice B

1. The graph of g is a translation 3 units up of the

graph of f.

2. The graph of g is a translation 5 units left of the

graph of f.

3. The graph of g is a translation 6 units left and

4 units down of the graph of f.

4. The graph of g is a translation 1 unit right and

5 units up of the graph of f.

5. The graph of g is a translation 4 units right and

3 units up of the graph of f.

6. The graph of g is a translation 8 units left and

2 units down of the graph of f.

7. The graph of g is a reflection in the x-axis, followed

by a horizontal stretch by a factor of 2 of the graph

of f.

8. The graph of g is a vertical shrink by a factor of 13,

followed by a translation 2 units up of the graph

of f.

Answers


A11

9. The graph of g is a vertical shrink by a factor of 13,

followed by a translation 1 unit left of the graph

of f.

10. The graph is a reflection in the x-axis, followed by

a vertical stretch by a factor of 3 and a translation

6 units left and 4 units down of the parent quadratic

function; ( 6, 4)

11. The graph is a vertical shrink by a factor of 13,

followed by a translation 2 units right and 1 unit up

of the parent quadratic function; (2, 1)

12. 2( 2)

( ) ; ( 2, 0)2

xg x

13. 2 43

( ) (3 4) 4; , 4g x x

14.


2 2 23 ; 3( 1) 1; 3( 1) 1;y x y x y x

2 23( 1) 1; 3( 4) 2;y x y x

2 23( 2) 2; 3( 2) 2y x y x

2.1 Puzzle Time

EL SALVADOR

2.2 Start Thinking

V shape; yes; yes; The line of symmetry is the y-axis.

2.2 Warm Up

1. (5, 3)P 2. ( 5, 3)P

3. ( 5, 15)P 4. (3, 3)P


1. linear; 11 ; 220;y x y After jogging for 20

minutes, 220 calories were burned.

2. not linear

2.2 Practice A

1. 2.

3. 4.

5.

( ) ( ) 3h x f x Add 3 to the output.

24 3 3x x Substitute ( )f x and simplify.

( ) ( )g x h x Multiply the input by 1.

24 3 3x x Substitute x into ( )h x

and simplify.

x −2 −1 0 1 2

( )f x 2 1 0 1 2

Answers


6.

7.

8.

9.

10.

11.

12.

13. Both graphs have the same axis of symmetry,

2.x

14. C; It has the largest leading coefficient, 3.a

15. minimum: 2; domain: all real numbers,

range: 2;y increasing to the right of 0;x

decreasing to the left of 0x




17. maximum: 3; domain: all real numbers,

range: 3;y increasing to the left of 2;x

decreasing to the right of 2x




19. a. noon b. 75 customers

2.2 Practice B

1. 2.

3. 4.

Answers


A13

5.

6.

7. 8.

9. 10.

11. 12.

13. lowest; The y-values on either side of 3x are

greater than 3.

14. A; Both have an axis of symmetry of 2.x










18. minimum: 2.5; domain: all real numbers,

range: 2.5;y increasing to the right of 3;x


19. a. The maximum height occurs 16

mile from the

base of the bridge.

b. The maximum height is 112

mile.


1. 23 6 1y x x 2. 2 2 1y x x

3. 22 8 1y x x 4. 23 6 3y x x

5. 2 2 5y x x 6. 212

2 2y x x

7. no; The definition of a quadratic function says

0,a but for the axis of symmetry to be

undefined, a would have to be 0.

8. Sample answer: ( 1, 10); The x-value 7 is 4 units

away from the vertex x-value 3. Because the

x-value 1 is also 4 units away from 3, it has the

same output value 10.

2.2 Puzzle Time

THIS BRITISH ROWER WAS THE FIRST WOMAN

TO ROW ACROSS THREE OCEANS.

2.3 Start Thinking

Sample answer:

yes; Point P is the same distance from the parabola as

the line 12

y is to the parabola. So, it will always

yield the same distance as long as the measurement is

taken from a point on the graph of the parabola.

Answers


2.3 Warm Up

1. 11.7 2. 3.2 3. 18

4. 7.3 5. 12.6 6. 14.3


1. 0.75

2

0.5

x

y

z

2. 8.125

8.5

2.625

x

y

z

2.3 Practice A

1. 218

y x 2. 2112

y x 3. 2124

y x

4. 2116

y x 5. 214

y x 6. 218

y x

7. A; The directrix is below the focus.

8. focus: (0, 3), directrix: 3,y

axis of symmetry: 0x



10. focus: (2, 0), directrix: 2,x

axis of symmetry: 0y

11. 12 in.; The receiver is at the focus.

12. 218

x y 13. 2116

x y 14. 213

y x

15. 2124

x y 16. 218

y x 17. 214

x y

18. vertex: (1, 3), focus: (1, 6), directrix: 0,y axis of

symmetry: 1;x The graph is a vertical shrink by

a factor of 13, followed by a translation 1 unit right

and 3 units up.

19. vertex: ( 5, 2), focus: ( 5, 4), directrix: 0,y

axis of symmetry: 5;x The graph is a vertical

shrink by a factor of 12, followed by a reflection in

the x-axis and a translation 5 units left and 2 units

down.

20. vertex: (2, 4), focus: (3, 4), directrix: 1,x

axis of symmetry: 4;y The graph is a

translation 2 units right and 4 units down.



shrink by a factor of 17

, followed by a reflection in

the x-axis and a translation 6 units left and 10 units

up.

2.3 Practice B

1. 2120

y x 2. 2124

y x 3. 2116

y x

4. 2132

y x 5. 2128

y x 6. 218

y x



Answers


A15







11. focus: 116

0, , directrix: 116

,y


12. focus: 18

0, , directrix: 18,y


13. 2112

y x 14. 218

y x 15. 2y x

16. 2148

x y 17. 2512

x y 18. 238

y x

19. 213

x y 20. 234

x y

21. vertex: ( 3, 2), focus: ( 7, 2), directrix: 1,x

axis of symmetry: 2;y The graph is a shrink

towards the y-axis by a factor of 14, followed by a

reflection in the y-axis and a translation 3 units left

and 2 units up.

22. vertex: 3132

( 2, 1), focus: 2, ,

3332

directrix: ,y axis of symmetry: 2;x

The graph is a vertical stretch by a factor of

32, followed by a translation 2 units left and 1 unit

down.

23. vertex: 11912120 120

(6, 3), focus: , 3 , directrix: ,x

axis of symmetry: 3;y The graph is a stretch

away from the y-axis by a factor of 20, followed by

a translation 6 units right and 3 units down.



shrink by a factor of 18, followed by a reflection

in the x-axis and a translation 1 unit left and 9 units

up.


1. 2

2

4

ax y 2. 2

8

ny x

3. 2

12

by x 4. 23

2

nx y

5. RS has a slope of 2 2 ( )( )

.s r s r s r

s r r ss r s r

OT has a slope of 2 20

.0

t tt

t t

Because and RS OT are parallel lines, their slopes

are equal.

So, .r s t

Answers


6. To find the midpoint of a line segment, find

the average of the x-values and y-values of

the endpoints.

The x-value of the midpoint of RS would be

.2

r s

The x-value of the midpoint OT would be .2

t

The x-value of the midpoint UV would be .2

u v

UV has as slope of

2 2

.v u v uv u

v u u vv u v u

Because UV is parallel to both RS and OT , all

slopes are equal and .u v r s t

So, the x-values of their midpoints are all the same

and lie on the same line, 2

tx or

2

r sx

or

.2

u vx

2.3 Puzzle Time

YELLOWSTONE PARK

2.4 Start Thinking

Sample answer:

y 110.25; After 25 weeks, you have $110.25 in your

bank account.

2.4 Warm Up

1. 16( 6)y x 2. 1

23 ( 1)y x

3. 1 2( 4)y x 4. 3 3( 3)y x

5. 14

18 ( 4)y x 6. 1 3( 6)y x


1.

The graph is a vertical stretch by a factor of 4,

followed by a translation 1 unit down of its parent

function.

2.


followed by a reflection in the x-axis of its parent

function.

3.


followed by a translation 7 units up of its parent

function.

4.

The graph is a reflection in the x-axis, followed by

a translation 2 units right and 23

unit down.

2.4 Practice A

1. 2716

( 2) 3y x 2. 2118

( 3) 8y x

3. 29( 1) 4y x 4. 85( 10)( 6)y x x

5. 316

( 2)( 8)y x x

6. 27( 14)( 2)y x x

Answers


A17

7. a. 259( 1) 5y x

b. 25 10 409 9 9

y x x

c. 59( 2)( 4)y x x

d. 25 10 409 9 9

y x x

e. yes; intercept form; Two intercepts were given.

8. 9.21 ft

2.4 Practice B

1. 219( 1) 6y x 2. 29

49( 2) 5x

3. 213( 1) 1y x

4. 53( 12)( 8)y x x

5. 116

( 7)( 1)y x x

6. 481

( 9)( 9)y x x

7. The two given sets of coordinates were not

substituted into the correct places.

2

2

12

( )

7 (1 3) 5

7 4 5

2 4

y a x h k

a

a

a

a

The equation is 12( 3) 5.y x

8. a. The maximum area of 2500 square feet occurs

when the length is 50 feet.

b. 2 2( ) 100 ; (2) 196 ftA x x x A

c. 0 to 50 ft: 2ft

50 ;ft

50 to 100 ft: 2ft

50ft


1. linear; 1.8 212.10y x

2. quadratic

a. 24.9 19.6 58.8y x x

b. 24.9( 2) 78.4y x

c. The graph of the function is a reflection in the

x-axis, followed by a vertical stretch by a factor

of 4.9 and a translation 2 units right and

78.4 units up of its parent function.

3. quadratic

a. 23 30 12y x x

b. 23( 5) 87y x



of 3 and a translation 5 units right and 87 units

up of its parent function.

4. linear; 0.433 14.7y x

5. quadratic

a. 25 14 3y x x

b. 25( 1.4) 12.8y x



of 5 and a translation 1.4 units right and

12.8 units up of its parent function.

2.4 Puzzle Time

PINK FLAMINGO

Cumulative Review

1. 18x 2. 15x 3. 12x

4. 26x 5. 75x 6. 2x

7. 3x 8. 12x 9. 21x

10. 9x 11. 8x 12. 6x

13. 26x 14. 7x 15. 8x

16. 45x

17. a. 89%

b. 95%

c. 55 correct answers

d. 60 correct answers

18. a. 89%

b. 75%

c. 24 correct answers

d. 26 correct answers

e. 22 correct answers

19. 3 cups 20. 4 tablespoons

21. 5.83 22. 7.07 23. 2.83

24. 10.44 25. 18.87 26. 7.07

27. 12.37 28. 7.21 29. 10.44

Answers


30. 19.24 31. 10.00 32. 10.00 33. 12.08

34. 17.03 35. 12.04 36. 353

37. 94

38. 3947 7

5 or 39. 2 40. 10

41. 8 42. 5 43. 3 44. 2

45. 18

3x y 46. 2 6x y

47. 15

7x y 48. 4 7x y

49. 83

2x y 50. 3 52 4

x y

51. 2 10x y 52. 14

5x y

53. 3 8x y 54. 14

x

55. no solution 56. no solution

57. no solution 58. 289

x

59. 6x 60. 812

x

61. 1003

x 62. 1x

63. 1009

x 64. 8x

65. no solution 66. 5 h

67. 2.25 h 68. about 52.5 h

69. 518 8

y x 70. 4 41y x

71. 12

4y x 72. 7 192 2

y x

73. 13 2210 5

y x 74. 3 207 7

y x

75. 3 375 5

y x 76. 19 218 4

y x

77. 4 17y x 78. 54

2y x

79. 23118 2

y x 80. 3 214 4

y x

81. 3 4114 14

y x 82. 2717 7

y x

83. 5 214 4

y x 84. ( 3)( 2)x x

85. ( 6)( 7)x x 86. ( 4)( 12)x x

87. ( 11)( 7)x x 88. ( 1)( 12)x x

89. ( 8)( 2)x x 90. ( 6)( 4)x x

91. ( 5)( 1)x x 92. ( 3)( 1)x x

93. ( 6)( 5)x x 94. ( 12)( 8)x x

95. ( 5)( 8)x x 96. (2 7)( 5)x x

97. (3 10)( 4)x x 98. (2 1)( 10)x x

99. (3 2)( 10)x x 100. (4 12)( 12)x x

101. (5 3)( 2)x x 102. (2 4)(3 11)x x

103. ( 9)(4 9)x x

104. (2 10)( 4) or 2 8 5x x x x

105. 2 4 32y x x

106. 24 4 48y x x

107. 22 2 4y x x

108. 26 6 72y x x

109. 25 55 120y x x

110. 23 9 84y x x

111. 26 36 54y x x

112. 27 14 7y x x

113. 22 16 32y x x

114. 2 8 17y x x

115. 2 10 18y x x

116. 2 16 73y x x

117. 23 6 7y x x

118. 27 70 178y x x

119. 29 54 74y x x

120. 24 64 261y x x

121. 22 20 51y x x

122. 23 6 2y x x

Answers


A19

123. 6 in. 124. 242 ft 125. 18 in.

126. 25184 in. 127. 2 3 6x i

128. 1 15x

129. 3 73

2x

130. 5 47

2

ix

131. 3 30x 132. 4 34x

133. 7 139

2x

134.

5 47

6

ix

135. 7 129

8x

136.

2 2 39

5

ix

137. 7 47

12

ix

138.

13 167

8

ix

139. 3 55

4

ix

140.

5 119

4

ix

141. 8 38

3

ix

142.

15 223

8

ix

143. 3 6x 144. 3 23

4

ix

145. 9 103

2x

146.

3 111

12

ix

147.

The graph of ( )g x is a vertical stretch by a factor

of 2 of the graph of ( ).f x

148.

The graph of ( )h x is a vertical shrink by a factor

of 12

and a reflection in the y-axis of the graph of

( ).f x

149.

The graph of ( )c x is a vertical translation 4 units

down of the graph of ( ).f x

150.

The graph of ( )d x is a vertical stretch by a factor

of 2 of the graph of ( ).f x

151.

The graph of ( )k x is a horizontal translation 4 units

left of the graph of ( ).f x

152. The graph of ( )m x is a

translation 3 units right

and 2 units up of the

graph of ( ).f x

Answers


153. ( ) 2 3g x x 154. 47

( ) 1g x x

155. ( ) 2 4g x x

156. 12

( ) 6 7g x x

157. ( ) 3 5g x x

158. ( ) 1 2g x x

159. ( ) 3 1g x x

160. 34

( ) 5g x x

Chapter 3

3.1 Start Thinking

Yes, there are patterns; Sample answer: A quadratic

equation has one x-intercept when the vertex is on the

x-axis. If the quadratic equation opens down, the graph

has two x-intercepts if the constant is positive and none

if the constant is negative. If the quadratic equation

opens up, the graph has two x-intercepts if the constant

is negative and none if the constant is positive; The

vertex is a minimum if the 2x term is positive; The

vertex is a maximum if the 2x term is negative.

3.1 Warm Up

1. 4, 2 2. 3, 4


4. no solution

5. 3 21

,11 11

or about 0.27, 1.91

6. 1, 2


1.

2.

3.

4.

3.1 Practice A

1. 5x and 1x 2. 3x

3. 5x and 5x 4. 2x and 6x

5. 4x and 4x 6. 3x and 1

2x

Equation Number of

x-intercepts Point(s)

2y x 1 0, 0

2y x 1 0, 0

2 4y x 2 2, 0 , 2, 0

2 4y x 0 N/A

Answers


A21

7. 10t and 10t 8. 8g and 8g

9. 2y and 6y

10. took the square root of each side before subtracting

16, and then incorrectly added the square roots of

the terms on the left side; 2

2 16 25;x

2

2 9;x 2 3;x 2 3;x 1x

and 5x

11. 2x and 2x 12. 2x and 3x

13. 0m and 4m 14. 9

15. 1 or 7

16. 2 10c and 2 10;c Sample answer:

square root property; There is no linear term.

17. 0v and 7;v Sample answer: factoring and

zero product property; The binomial is factorable.

18. no solution; left side always negative, right side

positive

19. 8x and 3;x Sample answer: factoring and

zero product property; The trinomial is factorable.

20. Sample answer: 2 10 24 0x x

3.1 Practice B

1. 1x and 1x 2. 1x and 1

3x

3. 7x and 2x 4. 3

4x and 3x

5. 2x and 6x 6. 3x and 6x

7. 14k and 8k

8. 1 3x and 1 3x

9. 3x and 3x

10. Sample answer:

a. 2

2 4 20x

b. 2

3 4 10x

c. 2

2 10 4x

11. 11x and 11x 12. 9k and 0k

13. 5w and 2w 14. 0y and 3y

15. 2

5x and

3;

5x Sample answer: Quadratic

Formula; The trinomial contains fractions.

16. 1.3n and 1.3;n Sample answer: square

root property; There is no linear term.

17. 2 and 9 18. 4 and 4

19. 0 and 13 20. 4

3

21. $30 per rental; $720

22. 216 15; 0.968 sech t t t


1. 12 units 2. 16 in.

3. 3 or 2 4. 7 units by 15 units

5. 16 and 14 or 14 and 16

6. 8 and 9 or 9 and 8

7. 24 and 22 or 22 and 24

8. 16 and 9 9. 15 years old

10. 15 units by 17 units 11. 1 ft

12. 6 ft by 12 ft 13. 25 in.

14. 10 cm

3.1 Puzzle Time

BUY A DECK OF CARDS

3.2 Start Thinking

Most calculators will show an error screen instead of

answering the keystrokes entered; There is no real

number answer to the expression. Most calculators are

not set up to consider the imaginary number set.

3.2 Warm Up

1. 10 32x 2. 10 58y

3. 12 18x 4. 12 64x

5. 7 10x 6. 12 82x

Answers



1. vertex: 4, 1 , focus: 3

4, ,4

directrix:

11,

4y axis of symmetry: 4x

2. vertex: 4, 0 , focus: 15

4, ,4

directrix:

15,

4y axis of symmetry: 4x

3. vertex: 3, 0 , focus: 3, 2 , directrix: 2,y


4. vertex: 4, 4 , focus: 4, 5 , directrix: 3,y


3.2 Practice A

1. 5i 2. 9i

3. 4 2i 4. 3x and 3y

5. 2x and 5y 6. 13x and 4y

7. 6x and 10y 8. 8 9i

9. 13 i 10. 2 2i

11. 3 i

12. a. 0 11i

b. 0 3 3 1 i

13. 10 20i 14. 9 24i

15. 7 i 16. 48 46i

17.

18. 3i and 3i 19. 7i and 7i

20. 6x i and 6x i

21. 2 5x i and 2 5x i

3.2 Practice B

1. 15i 2. 4 10i

3. 12 6i 4. 7x and 4y

5. 24x and 2y 6. 11x and 10y

7. 1x and 10

3y 8. 6 13i

9. 8 6i 10. 3 15i

11. 5 i

12. a. 2 3i

b. 4 4i

c. 5 2i

13. 6 43i 14. 34 0i

15. 149 0i 16. 20 48i

17.

18. 4 3i and 4 3i

19. 2 13i and 2 13i

20. 2 11x i and 2 11x i

21. 3 5x i and 3 5x i


1. 3 6

5 5i 2.

1 1

2 2i

3. 1 0i 4. 1 4

3 3i

5. 2 14

25 25i 6.

132 24

25 25i

[ 14 5 3 ] 4i i Definition of complex

addition

19 3 4i i Simplify.

19 3 4i i Definition of complex

addition

19 7i Write in standard form.

248 18 16 6i i i Multiply using FOIL.

248 34 6i i Simplify and use

2 1.i

48 34 6 1i Simplify.

42 34i Write in standard form.

Answers


A23

7−18.

19. Complex numbers and their conjugates are the

reflection of one another in the real axis.

20. 0,a so a bi is a pure imaginary number.

3.2 Puzzle Time

YOU’D KNOW THE DIFFERENCE IF YOU EVER

LET A PTERODACTYL SIT ON YOUR SHOULDER

3.3 Start Thinking

2 8 16;x x To find the middle term, multiply the

terms inside the parentheses and then multiply the result

by 2. To find the last term, square the second term

inside the parentheses; 22 6 9 3 ,a a a

22 14 49 7 ;b b b You could take the

coefficient of the middle term, divide it by 2, and then

square the result.

3.3 Warm Up

1. 5 5z y z y 2. 5 1 5 1x x

3. 2

7 2x y 4. 1 1

1 1x x

5. 2 2 1 2 1y y 6. 2

2 1r s


1. absolute value, domain: all real numbers, range:

0y

2. linear, domain: all real numbers, range: all real

numbers

3. quadratic, domain: all real numbers, range: 1y

4. absolute value, domain: all real numbers, range:

1y

5. linear, domain: all real numbers, range: all real

numbers

6. quadratic, domain: all real numbers, range:

5y

3.3 Practice A

1. 5x and 1x 2. 13y and 1y

3. 10 2 10n and 10 2 10n

4. 7 2p and 7 2p

5. 2

16; 4c x 6. 2

49; 7c x

7. 2

81; 9c y

8. 2

169; 13c y

9. 4 11x and 4 11x

10. 5 29h and 5 29h

11. 6 26t and 6 26t

12. 7 58s and 7 58s

13. 3 11y and 3 11y

14. 5 19g and 5 19g

15. square roots; Both sides are perfect squares; 8x

and 2x

16. factoring; factorable; 4x and 1x

17. Sample answer: factoring and square roots;

factorable, both sides are perfect squares; 3x

18. completing the square; even middle term;

5 33x and 5 33x

19. 4 20. 2 2 6

21. 2

5 7; 5, 7f x x

22. 2

3 11; 3, 11g x x

3.3 Practice B

1. 20w and 2w

2. 8 2 2k i and 8 2 2k i

3. 15 2 6t i and 15 2 6t i

Answers


4. 1 2 3

3p

and

1 2 3

3p

5. 2

64; 8c x 6.

249 7

;4 2

c x

7.

29 3

;4 2

c y

8. 2

100; 10c y

9. 3 10q and 3 10q

10. 1 13

2 2h

and

1 13

2 2h

11. 4 11x and 4 11x

12. 6y and 2y

13. 2 6t and 2 6t

14. 5 31

2 2s and

5 31

2 2s

15. square roots; Both sides are perfect squares;

16x and 2x

16. completing the square; not factorable;

211

3x

and

211

3x

17. Sample answer: factoring; factorable; 12x and

12x

18. factoring; factorable; 3x and 3x

19. 2

9 19; 9,19f x x

20. 2

1 27; 1, 27g x x

21. 2

11 25; 11, 25h x x

22. 2

1 7 1 7; ,

2 4 2 4f x x

23. a. 18 ft

b. 11

14

t sec or 1.8t sec


1. 2

4 0 0; 0, 0 ; 0f x x x

The graph is a vertical stretch by a factor of 4 of the


2. 2

0 3; 0, 3 ; 3 1.73f x x x

and 3 1.73x

The graph is a reflection in the x-axis followed by

a vertical translation 3 units up of the graph of the


3. 2

5 25 5 25; , ; 0

2 4 2 4f x x x

and

5x

The graph is a horizontal translation 5

2 units right

followed by a vertical translation 25

4 units down of

the graph of the parent quadratic function.

Answers


A25

4. 2

4 5; 4, 5 ;f x x

4 5 6.24x and

4 5 1.76x

The graph is a horizontal translation 4 units left

followed by a vertical translation 5 units down of

the graph of the parent quadratic function.

5. 2

3 1 6; 1, 6 ;f x x no x-intercepts

The graph is a reflection in the x-axis followed by

a vertical stretch by a factor of 3, and a horizontal

translation 1 unit right and vertical translation

6 units down of the graph of the parent quadratic

function.

6. 2

2 3 5; 3, 5 ;f x x

103 4.58

2x

and

103 1.42

2x

The graph is a vertical stretch by a factor of 2

followed by horizontal translation 3 units left and

vertical translation 5 units down of the graph of the


3.3 Puzzle Time

ONLINE SKATER

3.4 Start Thinking

Sample answer: completing the square: Use when

1a and b is even. Also, use when there is no c term;

factoring: Use when the function is easily factorable;

graphing: Use when the equation includes decimals or

when approximated answers are accepted; using square

roots: Use when the algebraic expression is a perfect

square; graphing, using square roots, factoring,

completing the square

3.4 Warm Up

1. 3

2 2. 1 3. 4

4. 4 5. 16 6. 6

5


1. 6 3g x x 2. 1

53

g x x

3.4 Practice A

1. 9 65

2x

2. 1x and 2x

3. 3x 4. 1

4x

and 1x

5. 5 23

6 6x i 6. 12x

7. 7 23

4 4x i

8.

1 5 2

3 6x i

9. 12; two real solutions 10. 0; one real solution

11. 207; two imaginary solutions

12. 16; two real solutions 13. B

14. Sample answer: 21; 16; 8 16 0a c x x

15. Sample answer: 22; 10; 2 5 10 0a c x x

16. 24 9 10 0x x 17. 23 11 2 0x x

18. 2

;3

x square root; perfect square

Answers


19. 3x and 1

;4

x Quadratic Formula; difficult to

factor

20. 6 3 3;x complete the square; even middle

term and leading coefficient of 1

21. 2x and 6;x factoring; easy to factor

22. 2 4 0

1 4 0

1

4

b ac

c

c

3.4 Practice B

1. 4x and 1x 2. 1x

3. 5 55

2 2x i 4.

3 89

8x

5. 6 51x 6. 66

13

x i

7. 5 21v 8. 4 2

3 3t i


10. 0; one real solution 11. 132; two real solutions


13. C

14. Sample answer: 21; 7; 3 7 0a c x x

15. Sample answer: 24; 12; 4 10 12 0a c x x

16. 27 10 6 0x x 17. 24 3 1 0x x

18. 1;x square root; perfect square after factoring

out 7

19. 10 6 3;x complete the square; even

middle term and leading coefficient of 1

20. 1 7

;2 2

x i Quadratic Formula; odd middle

term

21. 2x and 4;x factoring; easy to factor

22. 2 4 0

1 4 0

1

4

b ac

c

c


1. 1x and 1

;8

x yes

2. 5

2x

and

4;

3x yes

3. 1x and 7;x yes

4. 2

3x

and

4;

5x yes

5. 2.25x and 14;x yes

6. 2x and 20

;7

x yes

7. one real solution; 0x

8. two real solutions; 3x and 3x

9. two real solutions; 0x and 5x

Answers


A27

10. The average of the x-intercepts is the x-value of the

vertex.

3.4 Puzzle Time

SOFA SO GOOD

3.5 Start Thinking

Sample answer:

system with one linear equation and one quadratic

equation, two points of intersection:

system with two quadratic equations, one point of

intersection:

system with two quadratic equations, two points of

intersection:

3.5 Warm Up

1. 3.4, 1.4 2. 0, 0 3. 2, 1



1.

2.

3.

4.

3.5 Practice A

1. 6, 0 and 4, 2 2. 2, 3

3. 0, 3 and 1, 2 4. 1, 1 and 4, 5

5. 1, 2 6. no solution

7. 1, 3 and 4, 0 8. 0, 5 and 5, 0

9. 1, 0 10. 1

1,7 and , 74

11. 3, 8

Answers


12. 0.25, 7.5 and 1, 10

13. no solution 14. 3, 3 and 1, 3

15. The horizontal line cuts through the circle,

intersecting in two places.

3.5 Practice B

1. no solution 2. 1, 3 and 2, 6

3. 0, 9 and 3, 0 4. 1, 2

5. 0.27, 0 and 3.7, 0 6. 0, 6 and 2, 2

7. 1, 2 and 1, 2 8. 1, 0

9. no solution 10. 3, 2 and 2, 3

11. no solution 12. 8, 32 and 2, 2

13. 4, 24 and 2,12 14. 7

3, 8 and , 83

15. The horizontal line is tangent to the circle either at

the top or the bottom.


1. parabola; 29

1 34

y x

2. circle; 2 2

1 1 8x y

3. hyperbola;

2 22 3

15 20

x y

4. parabola; 2

3 4y x

5. circle; 2 2

1 3 25x y

6. hyperbola:

2 21 2

19 4

x y

3.5 Puzzle Time

SPUDNIK

3.6 Start Thinking

Sample answer:

Graph the parabola with 2 .y x bx c Make the

parabola dashed for inequalities with or and solid

for inequalities with or .

Test a point ,x y inside the parabola to determine

whether the point is a solution to the inequality.

Shade the region inside the parabola if the point is a

solution. Shade the region outside the parabola if the

point is not a solution.

3.6 Warm Up

1. 2.

3. 4.


1. 8

1

6

x

y

z

2. 2

4

7

x

y

z

3.6 Practice A

1. 2.

Answers


A29

3. 4.

5. y f x 6. y f x

7.

8.

9. 4 4

or3 3

x x 10. 1or 7x x

11. 7 3x 12. 9

12

x

13. all real numbers 14. 5.54 0.54x

15. 5 1x

16. 3.73 or 0.27x x

17. a. 2125 2500w w

b. 25 100w

3.6 Practice B

1.

2.

3.

4.

5. wrong side was shaded

6.

7.

Answers


8. 1

or 62

x x 9. 1

22

x

10. 3 13 or 3 13x x

11. 3 9x 12. 2.64 or 1.14x x

13. 1.66 0.91x 14. 3.24 1.24x

15. 4.37 or 1.37x x

16. a. 25 ft; 25h t when 0.t

b. 216 28 25 0t t

c. 0 0.65t


a. 22 370R x x x

b. $17,112

c. 92 or 93

d. 30 312C x x

e. 22 340 312 0P x x x

f. between 1 and 169, including 1 and 169

g. $14,138; 85 handbags

3.6 Puzzle Time

BAGELS

Cumulative Review

1. 5 2 2. 3 5 3. 4 6

4. 8 3 5. 10 3 6. 3 6

7. 5 7 8. 6 2 9. 5

6

10. 6

7 11.

3

2 12.

7

3

13. 1

4 14.

2

5 15.

7

9

16. 5

8 17. 3 18. 0

19. 2 20. 3 21. 11

22. 10 23. 67 24. 1

25. 46 5x 26. 28 22x

27. 27 12 8x x 28. 2 20 15x x

29. 33 24x 30. 2 25 35x x

31. 3 227 7 41 9x x x

32. 5 4 24 16 7 6x x x x

33. 3 28 10 22 19x x x

34. 4 3 210 35 19 8 20x x x x

35. a. 20.4 min b. 21 min c. 1.1 min

36. 24 40 44x x 37. 210 5 15x x

38. 2 6 8x x 39. 2 3 2x x

40. 220 5 90x x

41. 3 26 21 22 77x x x

42. 3 212 142 60 14x x x

43. 4 3 230 40 21 8 3x x x x

44. 3 284 164 79 9x x x

45. 4 3 24 30 116 99x x x x

46. 5 4 3 22 12 5 58 129 11x x x x x

47. 4 3 26 65 53 156 60x x x x

Number of

handbags

purchased

Price per

handbag

(dollars)

Revenue per

order

(dollars)

1 368 368

2 366 732

3 364 1092

4 362 1448

5 360 1800

6 358 2148

x 370 2x 370 2x x

Answers


A31

48. 24 28 12x x 49. 210 25 50x x

50. 2 16 48x x 51. 28 160 792x x

52. 23 6 9x x 53. 216 12 28x x

54. 296 444 462x x 55. 22 20 10x x

56. 27 23 17x x 57. 254 9 31x x

58. 26 47 28x x 59. 24 21 87x x

60. a. 95 items

b. 22 items

61. brother 7 min, sister 12 min

62. a. width 14 ft, length 19 ft

b. $1056

c. 266 ft2

63. 4, 7x x 64. 2, 3x x

65. 7, 9x x 66. 5

1,2

x x

67. 9

3,4

x x 68. 2

3,5

x x

69. 2 7

,3 5

x x 70. 5 7

,4 2

x x

71. 1 1

,4 6

x x 72. 3 1

,7 12

x x

73. 4 1

,7 4

x x 74. 1 9

,5 8

x x

75. 5

12,6

x x 76. 5 10

,2 11

x x

77. 4 6

,3 11

x x 78. 9y x

79. 1

52

y x 80. 3 17y x

81. 2 4y x 82. 11 23y x

83. 3 5

4 4y x 84. 6 3y x

85. 5 9y x 86. 14 21y x

87. 6 24y x 88. 2 28y x

89. 45 20y x 90. 108

91. 524 92. 448 93. 368

94. 57 95. 53 96. 20

97. 28 98. 279 99. 116

100. 73 101. 4

102. a. 4 18b b

b. 11 baskets

c. 7 baskets

103. a. 55 mi/h

b. 2.75 h

104. 8, 10x x 105. 34, 22x x

106. 0, 4x x 107. 14, 6x x

108. 13, 3x x 109. 9, 25x x

110. 11 13

,3 3

x x 111. 18, 12x x

112. no solution 113. 7, 3

114. 4, 2 115. no solution

116. 6, 6


118. 5, 7 119. 3, 4, 6

120. 9, 8, 2 121. 6, 2,1


123. 2, 1, 4 124. no solution

125. 6 15i 126. 12 10i

127. 5 5i 128. 7 18i

129. 9 7i 130. 12 8i

131. 2 2i 132. 2i

133. 26 3i 134. 11 22i

answers - mrshallalgebra2.files.wordpress.com · 2 5 followed by a translation 3 units right of the...

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