Alg1 RBC Answers A - Ms. Calvo's...

Answers

Algebra 1 Copyright © Big Ideas Learning, LLC Answers All rights reserved. A108

92.

93.

94. 7,1x = − 95. 13, 2x = − −

96. 3, 3x = − 97. 2, 5x = −

98. linear function: 3 10y x= +

99. quadratic function: 2 9y x= −

100. exponential function: 3xy =

Chapter 9 9.1 Start Thinking

360: 1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 18, 20, 24, 30, 36, 40, 45, 60, 72, 90, 120, 180, 360

Greatest perfect square: 36

360 36 10

36 10

6 10

= •

= •

=

9.1 Warm Up

1. 4 2. 8 3. 15

4. 45 5. 240 6. 6

7. 20 8. 2 9. 60

9.1 Cumulative Review Warm Up

1. exponential decay; 30%

2. exponential growth; 4%



9.1 Practice A

1. 5 2 2. 2 17 3. 7 2−

4. 3

5 5.

3

8− 6.

2

x−

7. 32 3 8. 35 2− 9. 34 2x x−

10. found square root instead of cube root

3 3

33

3

16 8 2

8 2

2 2

= •

= •

=

11. 5

5 12.

7

7

n

n 13.

3

3

3

3

14. 3 15. 9 5

5 16.

6

10

17. 4 w

w 18.

5

5

t

t 19.

14

7

z

20. 6 1

5

+ 21.

12 3 2

14

− 22.

5 3 6

23

+

23. 0.027

9.1 Practice B

1. 3 6 2. 5y 3. 3 2n n−

4. 29

10 5.

7

p p 6. 2

x

7. 232 4q 8. 3 9

2

d− 9. 3 260

9

x

y−

10. not fully simplified; the denominator contains a radical

30 30 30

25 525= =

11. 7

7

y

y 12.

3

3

k

k 13.

3 6

3 6

++

14. 4 3

3 15.

10

15 16.

6

6

t

t

x

y

4 8−4

10

x

y

4−4

−24

−12

Answers

Copyright © Big Ideas Learning, LLC Algebra 1 All rights reserved. Answers

A109

17. 35

7

h 18.

2

3 6

2

d

d 19.

325 2

2

20. 35 5 2

47

+ 21.

8 3 21

57

−

22. 5 35

2

− − 23.

3 323 3 3

1

x x

x

+ +−

9.1 Enrichment and Extension

1. 4 5i 2. 5 2iy x 3. 6 6i

4. 24 2iwz 5. 35 7ir pq 6. 22ix x

7. 5i 8. 2 3i 9. 10

5

i

10. 2 10i 11. 9i 12. 2 15ixy x

13. 3 10

4

i− 14. 3 2

2

i

− 15.

2iy

x

−

9.1 Puzzle Time

THANK YOU FERRY MUCH

9.2 Start Thinking

The parabola crosses the x-axis twice. The points are

( )1, 0− and ( )3, 0 .

The zeros of the function show the same points because a “zero” is another name for a point where the parabola crosses the x-axis. These points are called zeros because they represent the point(s) on the parabola where the y-value is zero.

9.2 Warm Up

1. 2x = − 2. 2b = 3. 4x =

4. 5y = − 5. 0y = 6. 1n =


1. 0 or 9x x= = 2. 0 or 2t t= = −

3. 0 or 10s s= = − 4. 2 or 4a a= − =

5. 1

2m = 6. 4 or 4g g= − =

9.2 Practice A

1. 1, 4x = − 2. 2, 5x =

3. 23 15 0x − = 4. 2 14 0x− + =

5. 22 4 5 0x x− + − = 6. 0, 3x = −

7. 1x = − 8. no solution

9. 5, 1x = − 10. no solution

11. 1, 3x = −

12. a. They indicate when the height is zero.

b. 4 ft

13. 6, 2x = − 14. 3, 5x = 15. 1, 10x = −

16.

0.4, 2.6x =

17.

0.8, 7.2x =

18.

7.6,1.6x = −

−5

5

−5

5

4

4

x

y

f(x) = x2 − 3x + 1

42 6

4

0

8

x

y

f(x) = −x2 + 8x − 6

x

y

−2−4

y = 13 x2 + 2x − 4

Answers


19.

no solution

20. 3 ftx =

9.2 Practice B

1. 3x = − 2. no solution

3. 2 23 0x− − = 4. 25 9 3 0x x− − + =

5. 27 2 6 0x x− − + = 6. 0, 6x =

7. 6x = 8. no solution

9. 1, 7x = − 10. no solution 11. 9, 1x = −

12. a. no; Time cannot be negative.

b. 2 sec

13. 7, 1x = − 14. 5, 4x = − − 15. 12, 2x = −

16.

4.6, 0.4x = − −

17.

1, 3x =

18.

no solution

19.

0.4, 5.6x =

20. 6 ft


1. a. 2.25 sec and 4 sec b. 6.25 sec

2. 60 ft 3. 8.5 years; in 1998

4. a. 1000 tires b. $35

9.2 Puzzle Time

IT HAS NO STEPS

x

y

−2

−2 2

y = −2x2 + 3x − 2

x

y

−4

−2

f(x) = x2 + 5x + 2

42

2

x

y

f(x) = x2 − 4x + 3

x

y

−2

2 4 6

y = 12 x2 − 3x + 1

x

y

−4

−2

2 4

y = −x2 + 3x − 5

Answers


A111

9.3 Start Thinking

Replacing ( )f x with zero and moving the constant

yields the following equations:

2 4x = 2 9x = 2 0x = 2 0x = 2 4x = −

2 9x = −

When the constant is positive, there are two solutions; when the constant is zero, there is one solution; and when the constant is negative, there are no solutions.

9.3 Warm Up

1. 5x = 2. 6x =

3. 2w = − 4. 2a = −


1. even 2. neither

3. neither 4. odd

9.3 Practice A

1. two; 6, 6x = − 2. zero

3. one; 0x = 4. 3, 3x = − 5. no solution

6. no solution 7. 8, 8x = − 8. 6, 6x = −

9. 0x = 10. 4x = 11. 5,1x = −

12. 8

, 23

x = − 13. 2.45x = ± 14. 4.24x = ±

15. 2.24x = ±

16. The square root does not distribute over subtraction,

so 2 9x − does not equal 3.x − Begin by

isolating 2x on the left side.

2

2

9 16

25

5

x

x

x

− =

== ±

17. a. 221 336w =

b. width 4 cm, length 12 cm

18. At 5,x = ± because 2 25.x =

19. At 1.1,x = ± because 2 1.21.x =

9.3 Practice B

1. two; 11,11x = − 2. zero

3. two; 14,14x = − 4. no solution

5. 2, 2x = − 6. 0x = 7. 3, 3x = −

8. 1 1,

3 3x = − 9.

9 9,

2 2x = − 10. 12, 2x = −

11. 1

, 22

x = − 12. 2 12

,5 5

x = −

13. 2.65x = ± 14. 2.83x = ± 15. 1.11x = ±

16. The right side becomes negative after subtracting 25, so the equation does not have a real solution.

2

2

25 9

16

x

x

+ =

= −

no solution

17. a. 210 160rπ π= b. 4 in.

18. a. 8, 2x = −

b. 12, 2x = −

c. 5, 5x = −


1. 0;x = multiplicity of 2; rational

2. ;x i= ± imaginary

3. 5 ;x i= ± imaginary

Function Number of zeroes

( ) 2 4f x x= − 2

( ) 2 9f x x= − 2

( ) 2f x x= 1

( ) 2f x x= − 1

( ) 2 4f x x= + 0

( ) 2 9f x x= + 0

Answers


4. 2 3;x = ± irrational

5. 6

;2

x = ± irrational

6. 2 3

;3

ix = ± imaginary

7. 2 ;x i= ± imaginary

8. 10

;2

ix = ± imaginary

9. 2 2 ;x i= ± imaginary

9.3 Puzzle Time

HOW ABOUT SECONDS

9.4 Start Thinking

The minimum and the vertex are the same point for the function.

A quadratic function has a minimum when the parabola opens up and a maximum when the parabola opens down; these correspond to positive and negative leading coefficients, respectively.

9.4 Warm Up

1. ( )( )3 3x x+ − 2. ( )21y +

3. ( )( )2 1 2 1x x+ − 4. ( )24x −

5. ( )22 1a + 6. ( )( )1 7 1 7x x+ −

7. ( )23 1a + 8. ( )2

2 5a −


1. 11z = 2. 4m = − 3. 2c =

4. 3y = − 5. 3g = − 6. 2h = −

7. 30n = 8. 19n = −

9.4 Practice A

1. 9c = 2. 25c = 3. 1c =

4. ( )22 4 4 2x x x− + = −

5. ( )22 20 100 10x x x− + = −

6. ( )22 26 169 13x x x+ + = +

7. 0.69, 8.69x = − 8. 1,11x =

9. 18.38, 0.38x = −

10. a. 2 12 160w w+ =

b. width 8 ft, length 20 ft

11. no solution 12. 5, 3x = −

13. 1.55, 6.45x = 14. 1, 7x = − −

15. 5.61,1.61x = − 16. 0.55, 5.45x =

17. Divide every term by 5.

18. minimum of 13− 19. minimum of 6−

20. maximum of 29 21. minimum of 40−

22. a. 2 2 224x x+ = b. 14− and 16−

9.4 Practice B

1. 64c = 2. 1

4c = 3.

49

4c =

4. ( )22 14 49 7x x x− + = −

5. ( )22 30 225 15x x x+ + = +

6. 2

2 81 99

4 2x x x

− + = −

7. 11.4,1.4x = − 8. 1.54, 4.54x = −

9. 15.76, 0.76x = −

10. a. 2 12 108− =

b. width 6 ft, length 18 ft

4 x

y

−2

2

(–2, –5)

x

y

−4

4

(1, –2)

Answers


A113

11. 2.17, 7.83x = 12. 20.8, 1.2x = − −

13. no solution 14. 19.17, 0.83x = − −

15. 5.61,1.61x = − 16. 1.37, 4.37x = −

17. 14b = ± 18. minimum at 5−

19. minimum at 39− 20. maximum at 9

4−

21. minimum at 5

22. a. 2 2 323x x+ =

b. 17 and 19


1. ( ) ( )21 5; 1, 5y x V= − +

2. ( ) ( )23 8; 3, 8y x V= + − − −

3. ( ) ( )21 4; 1, 4y x V= − + − − −

4. ( ) ( )23 1 1, 1, 1y x V= − − −

5. ( ) ( )22 3 3; 3, 3y x V= − +

6. ( ) ( )23 2 5; 2, 5y x V= − + − − −

7. ( ) ( )25 1 5; 1, 5y x V= + − − −

8. ( ) ( )214 1; 4, 1

2y x V= − − +

x2

y

4

x

y

2

−6

−4 −2

x2

y

−6

−2

−2

x

y

2

2

x

y

4

8

2 4

x

y

−4

−4 −2

x

y

−1

4

x

y

−4

4 8

Answers


9. ( ) ( )223 6; 3, 6

3y x V= + − − −

9.4 Puzzle Time

A HARE RESTORER

9.5 Start Thinking

When 0,a = the Quadratic Formula is undefined because you cannot divide by zero. In this case, the function has no 2x term, and is therefore not quadratic but linear.

The other situation that makes the Quadratic Formula undefined is when 2 4 0.b ac− < Note: In this case, the equation is technically still solvable, using the set of imaginary numbers.

9.5 Warm Up

1. 23 2. 361− 3. 477

4. 191 5. 39− 6. 0.699


1. 2 or 7w w≤ ≥

2. 5 1

3 3u− < < −

3. 4 0f− < <

4. 1 9

or5 5

v v≤ ≥

5. 7 17x− < <

6. no solution

9.5 Practice A

1. 2 5 0;x x+ = 1,a = 5,b = 0c =

2. 2 3 10 0;x x+ + = 1,a = 3,b = 10c =

3. 25 7 2 0;x x− − + = 5,a = − 7,b = − 2c =

4. 3x = − 5. no real solution

6. 1, 10x = − 7. 1

1,3

x = −

8. no real solution 9. 1

2x = −

10. 2 3

,3 2

x = − 11. 0.3, 2.1x = −

12. a. 0.3 and 0.8 sec b. 1.125 sec

13. one 14. two 15. zero

16. two 17. zero 18. two

19. 2;x = ± Using Square Roots; in the form 2x d=

20. no real solutions; Quadratic Formula; doesn’t fit the other methods

21. 0.4, 8.4;x = − completing the square; 1a = and

b is even.

22. 3.4, 2.4;x = − Quadratic Formula; doesn’t fit the

other methods

23. 7;x = factoring; Perfect Square Trinomial

24. 0, 5;x = factoring; easy to factor

25. a. 47 0;− < no real solutions

b. 23 5 6 0x x− + =

c. no; Both equations have zero solutions; the sign of b does not affect the discriminant because b is squared.

9.5 Practice B

1. 2 2 9 0;x x+ − = 1,a = 2,b = 9c = −

x

y

4

−6

−8 −4

0 3 6

2 7

9−3 12

0−2 −1 143

−53

− 23

− 23

13

− 13

0−2 642−6 −4

0−2 542 31−5 −4 −1−3

95

15

0 4 8

−7 17

12 16−4 20−8

Answers


A115

2. 27 6 1 0;x x− + − = 7,a = − 6,b = 1c = −

3. 24 10 7 0;x x− − = 4,a = 10,b = − 7c = −

4. 4x = 5. 1, 11x = −

6. 1

, 32

x = 7. 0.2, 0.8x = −

8. no real solution 9. 1x = −

10. 0.3, 1.4x = − 11. no real solution

12. a. 6.5 and 13.5 sec b. 21.2 sec

13. zero 14. two 15. one

16. one 17. zero 18. two

19. 20.6,x = 0.6;− completing the square; 1a =

and b is even.

20. 0,x = 3;− factoring; easy to factor

21. no real solution; using square roots; in the form 2x d=

22. 0.1,x = 1.4;− Quadratic Formula; doesn’t fit the

other methods

23. 1.1,x = − 1.9; Quadratic Formula; doesn’t fit the

other methods

24. 6;x = factoring; Perfect Square Trinomial

25. a. 47 0− < b. 23 5 6 0x x+ − =

c. yes; The original equation has zero solutions and the new equation has two solutions; changing the sign of c changes the discriminant from negative ( )47− to positive ( )97 .


1. 9 in.

2. length: 9 km, width: 12 km

3. width: 12 in., height: 16 in.

4. base: 22 4.7 in.,≈ height: 3 22 14.1 in.≈

5. height: 8 10 25.3 cm, base: 10 10 31.6 cm≈ ≈

9.5 Puzzle Time

THEIR TRUNKS

9.6 Start Thinking

System 1 has two solutions because the graphs of the equations intersect at two points.

System 2 has one solution because the graphs of the equations intersect at one point.

System 3 has no solution because the graphs of the equations do not intersect.

9.6 Warm Up

1. ( )1, 3− 2. ( )1, 3− −

3. ( )1, 1− 4. ( )2, 3


1.

x-intercept: ( )5, 0

5

−12

−5

12

= 2-10y x

=8y

6

−2

−4

8

= +44y x = 2+4 +4-y x x

5

−2

−5

6

= 2-3-4y x x

=6+2y x

2 6

−4

−2

x

y

Answers


2.

x-intercept: ( )0, 0

3.

x-intercept: ( )1, 0−

4.

x-intercept: 1

, 03

−

9.6 Practice A

1. ( ) ( )1, 2 , 0, 1− − 2. no real solution

3. ( )1, 3 4. ( ) ( )2, 1 , 4, 3− −

5. ( ) ( )0, 4 , 4, 0− 6. ( )2, 8

7. ( ) ( )7, 23 , 1, 5 8. ( ) ( )2, 1 , 5, 22− − −

9. ( ) ( )2, 1 , 1,2− − 10. ( ) ( )1, 4 , 3, 20− −

11. no real solution 12. ( ) ( )2, 4 , 2, 0−

13. a zero between 3− and 2− ; a zero between 1−

and 0

14. a zero between 1 and 3; a zero between 3 and 4

15. at 1.7t = sec

9.6 Practice B

1. ( ) ( )1, 5 , 2, 11− 2. ( ) ( )3, 10 , 0, 5−

3. ( )1, 4− 4. no real solution

5. ( )3, 18 6. no real solution

7. ( ) ( )7, 31 , 2, 4− − − 8. ( )0, 3−

9. ( )1, 1− 10. ( ) ( )3, 12 , 1, 4−

11. ( ) ( )1, 12 , 4, 7− 12. ( ) ( )3, 8 , 1, 0− −

13. a zero between 0 and 1

14. a zero between 0 and 1; a zero between 1 and 2

15. Sample answer: ( ) 21.6 2 5.6;f x x x= + −

( ) 22.5 2 4.2;g x x x= − − − corresponding

solutions are ( ) ( )1.25, 5.6 , 0.27, 4.93 .− − −


1. a. at 1t = sec, and then again at 3t = sec

b. 4.09 sec

2. 80, or 40 jackets 3. 435 items

4. a. yes

b. about 0.52 and 0.26 sec

5. a. about 0.59 sec

b. 1.07 sec

9.6 Puzzle Time

TO BE ABOVE IT ALL

Cumulative Review

1. 4x = −

2. 3, 4y y= − =

3. 5 4h− ≤ ≤

2 4

2

4

−4

−4 −2

x

y

2 4

2

4

−4

−2

−4

x

y

2 4

2

4

−4

−4 −2

x

y

0 4

−5

8−4−8

Answers


A117

4. 2y ≤

5. no solution

6. a. 350 1050y x≥ +

b. at least 4 h

7. 2 4 14x − ≥

8.

9.

10.

11. 1

32

y x= − + 12. 4 12y x= −

13. 1

162

y x= − − 14. ( )3, 2−

15. ( )6, 4− 16. no solution

17. $7 for a small box and $13 for a large box

18. 9

1

4x yz 19. 37m

20. yz

x 21. 1x =

22. 9x = 23. 10x = −

24. 4 13g− + 25. 3 2y −

26. 2 5 24x x+ − 27. 2 249 42 9x xy y+ +

28. 4, 6x = − 29. 0, 5g =

30. ( )( )4 2m m− − 31. ( )( )5 7z z+ −

32. ( )( )2 2 1w w+ + 33. 1 sec

34. 5, 5z z= − = 35. 11y = −

36. ( )( )23 4 5x x− − 37. ( )( )24 7 1y y− −

38.

vertical stretch by a factor of 5

39.

vertical shrink by a factor of 0.375

40.

vertical shrink by a factor of 3

7and a reflection in

the x-axis

0 6

2

12−6−12

1

2

−2 x

y

−1

4

2

x

y

−2

2−2 x

y

−2

2

2

−2 x

y

−2

2

2

−2 x

y

−2

4−4 x

y

−4

4

Answers


41.

translation 6 units up

42.

vertical stretch by a factor of 3, followed by a translation 7 units up

43.

vertical shrink by a factor of 1

,8

and a reflection in

the x-axis, followed by a translation 3 units down

44. a. 25 sec

b. If k is positive, it will increase part (a); if k is negative, it will decrease part (a).

45. a. axis of symmetry : 3x = −

b. vertex: ( )3, 30−

46. a. axis of symmetry: 5x =

b. vertex: ( )5, 80−

47.

domain : all real numbers; range: 1y ≥ −

48.

domain: all real numbers; range: 15y ≤

49. maximum: 4 50. minimum: 91−

51. vertex: ( )3, 0 ; axis of symmetry: 3x =

52. vertex: ( )5, 0 ;− axis of symmetry: 5x = −

53. vertex: ( )5, 4 ; axis of symmetry: 5x =

54.

translation 6 units to the left and a vertical stretch by a factor of 7

55.

translation 2 units to the right and 8 units down,

followed by a vertical shrink by a factor of 4

7

56.

2

4

8

12

−2 x

y

2

2

6

12

−2 x

y

4−4 x

y

−4

−2

2

2

−2 x

y

−2

2

16

8

−2 x

y

4

2

−8 −4 x

y

2 4

xy

−8

−2

x

y

−20

−30

−10

84−4−8

Answers


A119

57.

58. quadratic function; 2 4 12y x x= + −

59. 4 5y y 60. 2

3

61. 3 2 2 6− − 62. 3 2

3

2 4

5

x x

y

63. 5 30 3 2− + 64. 1

2

65. 9, 4x x= − = 66. 1, 1x x= − =

67. 5, 1x x= − = 68. 3, 4x x= =

69. 4x = ± 70. 5x = ±

71. no real solutions 72. 2 sec

73. 2, 1x x= − = − 74. 2, 10y y= − = −

75. 17.3, 1.3w w≈ − ≈ 76. 7, 3t t= − = −

77. 2, 4n n= − = 78. 8

4,3

h h= − = −

79. a square fence, with side length 15 ft

80. 3 1

,2 2

x x= − = − 81. 5

4,2

y y= − =

82. 0.4, 3.9w w= − = 83. 1.8, 1.3z z= − =

84. 0 x-intercepts 85. 1 x-intercept

86. 2 x-intercepts 87. 0 x-intercepts

88. ( )2, 2− and ( )4, 10− 89. ( )2, 4− − and ( )1, 1−

90. no solution 91. 3 in. by 12 in.

Chapter 10 10.1 Start Thinking

The domain of the function is all positive real numbers and zero. The range is also all positive real numbers and zero. You cannot use negative numbers in the domain because the square root function cannot be evaluated using negative numbers in this course.

The calculator is able to graph this function because negative numbers and zero will allow the radical to be evaluated. This function has an inverse domain when compared to .y x=

10.1 Warm Up

1.

2.

x

y4

−12

84−4−8

5

−5

−5

5

5

−5

−5

5

−2

−4

2 4 x

y

−2−4

3

−2

−4

2 4 x

y

−2−4

4

2

Alg1 RBC Answers A - Ms. Calvo's...

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