ANSWER: {–8.45, –3.55}
4-5 Completing the Square
Solve each equation by using the Square Root
Property. Round to the nearest hundredth if
necessary.
2. SOLUTION: 1. Factor the perfect square trinomial.
SOLUTION: Factor the perfect square trinomial.
Use the Square Root Property.
Use the Square Root Property.
The solution set is {0.39, 7.61}.
The solution set is {–8.45, –3.55}.
ANSWER: {0.39, 7.61}
ANSWER: {–8.45, –3.55}
3. SOLUTION: 2. SOLUTION: Factor the perfect square trinomial.
Factor the perfect square trinomial.
Use the Square Root Property.
Use the Square Root Property.
The solution set is {–12.87, –5.13}.
The solution set is {0.39, 7.61}.
eSolutions Manual - Powered by Cognero
ANSWER: ANSWER: {–12.87, –5.13}
Page 1
ANSWER: {0.39, 7.61} the Square
4-5 Completing
ANSWER: {–12.87, –5.13}
3. 4. SOLUTION: SOLUTION: Factor the perfect square trinomial.
Factor the perfect square trinomial.
Use the Square Root Property.
Use the Square Root Property.
The solution set is {–12.87, –5.13}.
ANSWER: {–12.87, –5.13}
4. SOLUTION: Factor the perfect square trinomial.
Use the Square Root Property.
The solution set is {–2.77, –0.56}.
ANSWER: {–2.77, –0.56}\
5. LASER LIGHT SHOW The area A in square feet
2
of a projected laser light show is given by A = 0.16d ,
where d is the distance from the laser to the screen
in feet. At what distance will the projected laser light
show have an area of 100 square feet?
SOLUTION: Substitute 100 for A, and find the value of d.
Use the Square Root Property.
d cannot be negative.
Manual - Powered by Cognero
eSolutions
The solution set is {–2.77, –0.56}.
So, the distance is 25 feet.
ANSWER: Page 2
ANSWER: ANSWER: {–2.77, –0.56}\
4-5 Completing
the Square
2
25; (x – 5)
5. LASER LIGHT SHOW The area A in square feet
2
7. of a projected laser light show is given by A = 0.16d ,
where d is the distance from the laser to the screen
in feet. At what distance will the projected laser light
show have an area of 100 square feet?
SOLUTION: To find the value of c, divide the coefficient of x by 2
and square the result.
So:
c = 6.25
Substitute 6.25 for c in the trinomial.
SOLUTION: Substitute 100 for A, and find the value of d.
Use the Square Root Property.
ANSWER: 2
6.25; (x – 2.5)
d cannot be negative.
Solve each equation by completing the square.
So, the distance is 25 feet.
ANSWER: 25 ft
8. SOLUTION: Find the value of c that makes each trinomial a
perfect square. Then write the trinomial as a
perfect square.
6. SOLUTION: To find the value of c, divide the coefficient of x by 2
and square it.
So:
c = 25
Substitute 25 for c in the trinomial.
Use the Square Root Property.
The solution set is {–4, 2}.
ANSWER: {–4, 2}
ANSWER: 25; (x – 5)
2
9. 7. eSolutions Manual - Powered by Cognero
SOLUTION: To find the value of c, divide the coefficient of x by 2
SOLUTION: Page 3
ANSWER: {–4, 2}
4-5 Completing
the Square
ANSWER: 9. 10. SOLUTION: SOLUTION: Use the Square Root Property.
Use the Square Root Property.
The solution set is
.
ANSWER: The solution set is { –0.69, 2.19}.
10. ANSWER: {–0.69, 2.19}
SOLUTION: 11. SOLUTION: Use the Square Root Property.
Use the Square Root Property.
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eSolutions
The solution set is { –0.69, 2.19}.
Page 4
ANSWER: {–0.69, 2.19}the Square
4-5 Completing
ANSWER: {–4.37, 1.37}
11. 12. SOLUTION: SOLUTION: Use the Square Root Property.
Use the Square Root Property.
The solution set is
ANSWER: The solution set is { –4.37, 1.37}.
13. ANSWER: {–4.37, 1.37}
SOLUTION: 12. SOLUTION: Use the Square Root Property.
Use the Square Root Property.
ANSWER: {–6.45, –1.55}
Solve each equation by using the Square Root
Property. Round to the nearest hundredth if
necessary.
The solution set is
eSolutions
Manual - Powered by Cognero
ANSWER: 14. Page 5
ANSWER: {–6.45, –1.55}
4-5 Completing
the Square
ANSWER: {–1.47, 7.47}
Solve each equation by using the Square Root
Property. Round to the nearest hundredth if
necessary.
16. SOLUTION: 14. SOLUTION: Use the Square Root Property.
Use the Square Root Property.
The solution set is {–8.24, 0.24}.
ANSWER: {–8.24, 0.24}
The solution set is { –5.16, 1.16}.
ANSWER: {–5.16, 1.16}
17. SOLUTION: 15. SOLUTION: Use the Square Root Property.
The solution set is {–7.65, –2.35}.
ANSWER: {–7.65, –2.35}
ANSWER: {–1.47, 7.47}
18. 16. SOLUTION: SOLUTION: eSolutions Manual - Powered by Cognero
Use the Square Root Property.
Page 6
ANSWER: {–7.65, –2.35}
4-5 Completing
the Square
ANSWER: {–1, 3}
18. 20. SOLUTION: SOLUTION: Use the Square Root Property.
Use the Square Root Property.
The solution set is {0.5, 4.5}.
The solution set is {–8.24, –3.76}.
ANSWER: {–8.24, –3.76}
ANSWER: {0.5, 4.5}
21. 19. SOLUTION: SOLUTION: Use the Square Root Property.
Use the Square Root Property.
The solution set is {–1, 3}.
The solution set is {4.67, 10.33}.
ANSWER: {–1, 3}
ANSWER: {4.67, 10.33}
20. SOLUTION: 22. SOLUTION: Manual - Powered by Cognero
eSolutions
Use the Square Root Property.
Page 7
Use the Square Root Property.
ANSWER: {4.67, 10.33}the Square
4-5 Completing
ANSWER: {–0.95, 3.95}
22. 24. SOLUTION: SOLUTION: Use the Square Root Property.
Use the Square Root Property.
The solution set is {–17, –15}.
ANSWER: {–17, –15}
The solution set is {–5.5, –1.5}.
ANSWER: {–5.5, –1.5}
23. 25. SOLUTION: SOLUTION: Use the Square Root Property.
Use the Square Root Property.
The solution set is {–0.95, 3.95}
The solution set is {4, 5}
.
ANSWER: {–0.95, 3.95}
ANSWER: {4, 5}
24. Find the value of c that makes each trinomial a
perfect square. Then write the trinomial as a
perfect square.
SOLUTION: eSolutions Manual - Powered by Cognero
Page 8
26. .
ANSWER: ANSWER: {4, 5}
4-5 Completing
the Square
2
64; (x + 8)
Find the value of c that makes each trinomial a
perfect square. Then write the trinomial as a
perfect square.
28. SOLUTION: To find the value of c, divide the coefficient of x by
2, and square it.
26. SOLUTION: To find the value of c, divide the coefficient of x by
2, and square the result.
Substitute
in the trinomial.
Substitute 16 for c in the trinomial.
ANSWER: ANSWER: 2
16; (x + 4)
27. 29. SOLUTION: To find the value of c, divide the coefficient of x by
2, and square it.
SOLUTION: To find the value of c, divide the coefficient of x by
2, and square it.
Substitute 64 for c in the trinomial.
Substitute c = 20.25 in the trinomial.
ANSWER: ANSWER: 2
64; (x + 8)
20.25; (x + 4.5)
28. Solve each equation by completing the square.
SOLUTION: To find the value of c, divide the coefficient of x by
2, and square it.
eSolutions Manual - Powered by Cognero
2
30. SOLUTION: Page 9
ANSWER: ANSWER: {– 4.61, 2.61}
2
20.25; (x + 4.5)
4-5 Completing
the Square
Solve each equation by completing the square.
32. 30. SOLUTION: SOLUTION: Use the Square Root Property.
Use the Square Root Property.
;
The solution set is
The solution set is {– 4, – 2}
.
.
ANSWER: {– 4, – 2}
ANSWER: 33. 31. SOLUTION: SOLUTION: Use the Square Root Property.
Use the Square Root Property.
The solution set is {1, 3}.
The solution set is {–4.61, 2.61}.
ANSWER: {1, 3}
ANSWER: {– 4.61, 2.61}
32. eSolutions Manual - Powered by Cognero
SOLUTION: 34. SOLUTION: Page 10
ANSWER: ANSWER: {1, 3}
4-5 Completing
the Square
34. 35. SOLUTION: SOLUTION: Use the Square Root Property.
Use the Square Root Property.
The solution set is
.
The solution set is
.
ANSWER: ANSWER: 35. SOLUTION: 36. SOLUTION: Use the Square Root Property.
The solution set is
eSolutions Manual - Powered by Cognero
ANSWER: .
Page 11
ANSWER: The solution set is {–1, 3}.
ANSWER: {–1, 3}
4-5 Completing the Square
36. 38. SOLUTION: SOLUTION: The solution set is
.
The solution set is
ANSWER: .
ANSWER: 39. SOLUTION: 37. SOLUTION: The solution set is
.
[
ANSWER: The solution set is {–1, 3}.
ANSWER: {–1, 3}
40. SOLUTION: 38. SOLUTION: eSolutions Manual - Powered by Cognero
Page 12
The solution set is
.
ANSWER: ANSWER: ]{5 – 2i, 5 + 2i}
4-5 Completing the Square
40. 42. SOLUTION: SOLUTION: The solution set is
.
ANSWER: {3 – 3i, 3 + 3i}
The solution set is
.
ANSWER: {–0.39, 1.72}
41. SOLUTION: 43. SOLUTION: The solution set is
.
ANSWER: ]{5 – 2i, 5 + 2i}
Use the Square Root Property.
42. SOLUTION: The solution set is
.
ANSWER: eSolutions Manual - Powered by Cognero
Page 13
The solution set is
.
ANSWER: ANSWER: {–0.39, 1.72}the Square
4-5 Completing
43. 44. SOLUTION: SOLUTION: ]
Use the Square Root Property.
The solution set is {–0.71, 3.11}.
ANSWER: {–0.71, 3.11}
45. The solution set is
.
SOLUTION: ANSWER: The solution set is
.
44. ANSWER: SOLUTION: ]
46. SOLUTION: The solution set is {–0.71, 3.11}.
ANSWER: {–0.71, 3.11}
eSolutions Manual - Powered by Cognero
45. Page 14
ANSWER: ANSWER: {–0.89, 5.39}
4-5 Completing the Square
46. SOLUTION: 48. CCSS MODELING An architect’s blueprints call
for a dining room measuring 13 feet by 13 feet. The
customer would like the dining room to be a square,
but with an area of 250 square feet. How much will
this add to the dimensions of the room?
SOLUTION: The area of a square is given by
the side length.
, where s is
Therefore:
The solution set is {–1.39, 1.59}.
ANSWER: {–1.39, 1.59}
Solve for x.
Therefore, about 2.81 ft should be added to the
dimensions of the room.
47. ANSWER: about 2.81 ft
SOLUTION: Solve each equation. Round to the nearest
hundredth if necessary.
49. SOLUTION: Write the equation in standard form and solve using
the quadratic formula.
The quadratic formula is given by:
The solution set is {–0.89, 5.39}.
ANSWER: {–0.89, 5.39}
48. CCSS MODELING An architect’s blueprints call
for aManual
dining- Powered
room measuring
eSolutions
by Cognero 13 feet by 13 feet. The
customer would like the dining room to be a square,
but with an area of 250 square feet. How much will
this add to the dimensions of the room?
The solution set is {2.38, 4.62}.
Page 15
dimensions of the room.
ANSWER: {2.38, 4.62}
ANSWER: about 2.81 ft the Square
4-5 Completing
Solve each equation. Round to the nearest
hundredth if necessary.
50. SOLUTION: Write the equation in standard form and solve using
the quadratic formula.
49. SOLUTION: Write the equation in standard form and solve using
the quadratic formula.
The quadratic formula is given by:
The quadratic formula is given by:
The solution set is {–2.77, –0.56}.
The solution set is {2.38, 4.62}.
ANSWER: {–2.77, –0.56}
ANSWER: {2.38, 4.62}
51. 50. SOLUTION: Write the equation in standard form and solve using
the quadratic formula.
The quadratic formula is given by:
SOLUTION: Write the equation in standard form and solve using
the quadratic formula.
The quadratic formula is given by:
The solution set is {–2.77, –0.56}.
eSolutions Manual - Powered by Cognero
ANSWER: The solution set is {0.26, –1.26}.
ANSWER: Page 16
ANSWER: {–1.26, 0.26}
ANSWER: {–2.77, –0.56}
4-5 Completing
the Square
52. 51. SOLUTION: Write the equation in standard form and solve using
the quadratic formula.
SOLUTION: Write the equation in standard form and solve using
the quadratic formula.
The quadratic formula is given by:
The quadratic formula is given by:
The solution set is {–1.44, 0.24}.
The solution set is {0.26, –1.26}.
ANSWER: {–1.26, 0.26}
52. SOLUTION: Write the equation in standard form and solve using
the quadratic formula.
The quadratic formula is given by:
ANSWER: {–1.44, 0.24}
53. FIREWORKS A firework’s distance d meters from
2
the ground is given by d = –1.5t + 25t, where t is the
number of seconds after the firework has been lit.
a. How many seconds have passed since the
firework was lit when the firework explodes if it
explodes at the maximum height of its path?
b. What is the height of the firework when it
explodes?
SOLUTION: a. The maximum occurs at the vertex.
Find the x-coordinate of the vertex.
The x-coordinate of the vertex is given by
.
Here, a = –1.5 and b = 25.
Therefore:
The solution set is {–1.44, 0.24}.
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eSolutions
ANSWER: Page 17
a.
seconds
ANSWER: {–1.44, 0.24}the Square
4-5 Completing
b. about 104.2 ft
Find the value of c that makes each trinomial a
perfect square. Then write the trinomial as a
perfect square.
53. FIREWORKS A firework’s distance d meters from
2
the ground is given by d = –1.5t + 25t, where t is the
number of seconds after the firework has been lit.
54. a. How many seconds have passed since the
firework was lit when the firework explodes if it
explodes at the maximum height of its path?
SOLUTION: To find the value of c, divide the coefficient of x by 2
and square it.
b. What is the height of the firework when it
explodes?
SOLUTION: a. The maximum occurs at the vertex.
Find the x-coordinate of the vertex.
Substitute the value of c in the trinomial.
The x-coordinate of the vertex is given by
.
Here, a = –1.5 and b = 25.
Therefore:
ANSWER: 2
0.1225; (x + 0.35)
55. That is
SOLUTION: To find the value of c, divide the coefficient of x by 2
and square it.
seconds should have passed when the
firework explodes at the maximum height.
b. Substitute
for t in the equation and solve for d.
Substitute the value of c in the trinomial.
The height of the firework is about 104.2 ft.
ANSWER: ANSWER: a.
seconds
2
2.56; (x – 1.6)
b. about 104.2 ft
FindManual
the value
of cbythat
makes
eSolutions
- Powered
Cognero
each trinomial a
perfect square. Then write the trinomial as a
perfect square.
56. Page 18
SOLUTION: To find the value of c, divide the coefficient of x by 2
• Extend
point Q.
ANSWER: until it intersects the arc. Label this 2
• Construct rectangle ARQD.
2.56; (x – 1.6)
4-5 Completing
the Square
b. ALGEBRAIC Let AD = x and CQ = 1. Use
56. completing the square to solve
for x.
SOLUTION: To find the value of c, divide the coefficient of x by 2
and square it.
c. TABULAR Make a table of x and values for CQ
= 2, 3, and 4.
d. VERBAL What do you notice about the xvalues? Write an equation you could use to determine
x for CQ = n, where n is a nonzero real number.
Substitute the value of c in the trinomial.
SOLUTION: a.
ANSWER: 57. MULTIPLE REPRESENTATIONS In this
problem, you will use quadratics to investigate golden
rectangles and the golden ratio.
a. GEOMETRIC
Therefore, DQ = x + 1.
• Draw square ABCD.
Substitute.
• Locate the midpoint of
b. AD = x. So, QR = x
CQ = 1
. Label the midpoint P.
• Draw
• Construct an arc with a radius of
from B
clockwise past the bottom of the square.
• Extend
point Q.
until it intersects the arc. Label this • Construct rectangle ARQD.
b. ALGEBRAIC Let AD = x and CQ = 1. Use
completing the square to solve
x cannot be negative.
So:
for x.
eSolutions Manual - Powered by Cognero
c. TABULAR Make a table of x and values for CQ
= 2, 3, and 4.
c.
Page 19
d. Sample answer: the x-values are multiples of
x cannot be negative.
4-5 Completing
the Square
So:
58. ERROR ANALYSIS Alonso and Aida are solving
2
x + 8x – 20 = 0 by completing the square. Is either
of them correct? Explain your reasoning.
c.
d. Sample answer: the x-values are multiples of
;
ANSWER: a.
b.
SOLUTION: Alonso; Aida did not add 16 to each side; she added
it only to the left side.
c.
ANSWER: Alonso; Aida did not add 16 to each side; she added
it only to the left side.
d. Sample answer: the x-values are multiples of
2
58. ERROR ANALYSIS Alonso and Aida are solving
2
x + 8x – 20 = 0 by completing the square. Is either
of them correct? Explain your reasoning.
59. CHALLENGE Solve x + bx + c = 0 by completing
the square. Your answer will be an expression for x
in terms of b and c.
SOLUTION: eSolutions Manual - Powered by Cognero
Page 20
ANSWER: Alonso; Aida did not add 16 to each side; she added
it only to the the
left side.
4-5 Completing
Square
e . 16(x + 2)2 = 0 2
2
f. (x + 4) = (x + 6)
2
59. CHALLENGE Solve x + bx + c = 0 by completing
the square. Your answer will be an expression for x
in terms of b and c.
SOLUTION: Use the Square Root Property.
SOLUTION: a. 2; rational; 16 is a perfect square so x + 2 and x
are rational.
b. 2; rational; 16 is a perfect square so x – 2 and x
are rational.
c. 2; complex; If the opposite of square is positive,
the square is negative. The square root of a negative
number is complex.
d. 2; real; The square must equal 20. Since that is
positive but not a perfect square, the solutions will be
real but not rational.
e . 1; rational; The expression must be equal to 0 and
only -2 makes the expression equal to 0.
f. 1; rational; The expressions (x + 4) and (x + 6)
must either be equal or opposites. No value makes
them equal, -5 makes them opposites. The only
solution is -5.
ANSWER: a. 2; rational; 16 is a perfect square so x + 2 and x
are rational.
b. 2; rational; 16 is a perfect square so x – 2 and x
are rational.
c. 2; complex; If the opposite of square is positive,
the square is negative. The square root of a negative
number is complex.
d. 2; real; The square must equal 20. Since that is
positive but not a perfect square, the solutions will be
real but not rational.
e . 1; rational; The expression must be equal to 0 and
only -2 makes the expression equal to 0.
f. 1; rational; The expressions (x + 4) and (x + 6)
must either be equal or opposites. No value makes
them equal, -5 makes them opposites. The only
solution is -5.
e . 16(x + 2)2 = 0 ANSWER: 60. CCSS ARGUMENTS Without solving, determine
how many unique solutions there are for each
equation. Are they rational, real, or complex? Justify
your reasoning.
a. (x + 2)2 = 16 2
b. (x - 2) = 16 c. -(x - 2)2 = 16
2
d. 36 - (x - 2) = 16 2
2
f. (x + 4) = (x + 6)
SOLUTION: a. 2; rational; 16 is a perfect square so x + 2 and x
are rational.
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61. OPEN ENDED Write a perfect square trinomial
equation in which the linear coefficient is negative
and the constant term is a fraction. Then solve the
equation.
SOLUTION: Page 21
f. 1; rational; The expressions (x + 4) and (x + 6)
must either be equal or opposites. No value makes
them equal, -5 makes them opposites. The only
solution is -5.the Square
4-5 Completing
Completing the square allows you to rewrite one side
of a quadratic equation in the form of a perfect
square. Once in this form, the equation can be solved
by using the Square Root Property.
61. OPEN ENDED Write a perfect square trinomial
equation in which the linear coefficient is negative
and the constant term is a fraction. Then solve the
equation.
2
2
63. SAT/ACT If x + y = 2xy, then y must equal
A –1
B 0
SOLUTION: Sample answer:
C 1
D –x
E x
The solution set is
.
SOLUTION: ANSWER: Sample answer:
62. WRITING IN MATH Explain what it means to
complete the square. Include a description of the
steps you would take.
SOLUTION: Completing the square allows you to rewrite one side
of a quadratic equation in the form of a perfect
square. Once in this form, the equation can be solved
by using the Square Root Property.
The correct choice is E.
ANSWER: E
64. GEOMETRY Find the area of the shaded region.
ANSWER: Completing the square allows you to rewrite one side
of a quadratic equation in the form of a perfect
square. Once in this form, the equation can be solved
by using the Square Root Property.
2
F 14 m
2
2
63. SAT/ACT If x + y = 2xy, then y must equal
A –1
B 0
C 1
G 18 m2
2
H 42 m
J 60 m2
SOLUTION: The area of the outer rectangle is given by:
D –x
eSolutions
E xManual - Powered by Cognero
Page 22
SOLUTION: The area of the inner rectangle is given by:
ANSWER: E
4-5 Completing
the Square
ANSWER: H
64. GEOMETRY Find the area of the shaded region.
65. SHORT RESPONSE What value of c should be
used to solve the following equation by completing
the square?
SOLUTION: 2
F 14 m
G 18 m2
2
H 42 m
ANSWER: 125
J 60 m2
SOLUTION: The area of the outer rectangle is given by:
2
66. If 5 – 3i is a solution for x + ax + b = 0, where a
and b are real numbers, what is the value of b?
A 10
The area of the inner rectangle is given by:
B 14
C 34
D 40
The area of the shaded region is
.
SOLUTION: Substitute 5 – 3i for x in the equation.
The correct choice is H.
Equate the real and the imaginary parts.
ANSWER: H
65. SHORT RESPONSE What value of c should be
used to solve the following equation by completing
the square?
And:
Substitute a = –10.
The correct choice is C.
SOLUTION: ANSWER: C
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Page 23
ANSWER: 39 + 80i
ANSWER: 125
4-5 Completing
the Square
2
66. If 5 – 3i is a solution for x + ax + b = 0, where a
and b are real numbers, what is the value of b?
68. SOLUTION: A 10
B 14
C 34
ANSWER: 24 – 34i
D 40
SOLUTION: Substitute 5 – 3i for x in the equation.
69. SOLUTION: Equate the real and the imaginary parts.
And:
Substitute a = –10.
ANSWER: The correct choice is C.
ANSWER: C
Simplify.
Write a quadratic equation in standard form with
the given root(s).
67. 70. SOLUTION: SOLUTION: ANSWER: 39 + 80i
ANSWER: 2
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68. 20x – 31x + 12 = 0
Page 24
ANSWER: ANSWER: 2
5x – 28x – 12 = 0
4-5 Completing the Square
Write a quadratic equation in standard form with
the given root(s).
72. 70. SOLUTION: SOLUTION: ANSWER: ANSWER: 2
20x – 31x + 12 = 0
71. SOLUTION: 2
28x + 31x + 6 = 0
73. TRAVEL Yoko is going with the Spanish Club to
Costa Rica. She buys 10 traveler’s checks in
denominations of $20, $50, and $100, totaling $370.
She has twice as many $20 checks as $50 checks.
How many of each denomination of traveler’s
checks does she have?
SOLUTION: Let x, y, and z represent the number of $20, $50, and
$100 checks respectively.
So: x + y + z = 10
And: 20x + 50y + 100z = 370
ANSWER: 2
Also: x = 2y
5x – 28x – 12 = 0
Solve the equations.
x = 6, y = 3, and z = 1.
72. Therefore, Yoko has 1-$100, 3-$50, and 6-$20
checks.
SOLUTION: ANSWER: 1 $100, 3 $50, and 6 $20 checks
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74. SHOPPING Main St. Media sells all DVDs for one
price and all books for another price. Alex bought 4
DVDs and 6 books for $170, while Matt boughtPage
3 25
DVDs and 8 books for $180. What is the cost of a
DVD and the cost of a book?
ANSWER: 1 $100, 3 $50,the
andSquare
6 $20 checks
4-5 Completing
ANSWER: DVD: $20; book: $15
74. SHOPPING Main St. Media sells all DVDs for one
price and all books for another price. Alex bought 4
DVDs and 6 books for $170, while Matt bought 3
DVDs and 8 books for $180. What is the cost of a
DVD and the cost of a book?
Graph each inequality.
75. SOLUTION: The boundary of the graph is the graph of y = 4x – 3.
Since the inequality symbol is , the line will be solid.
Test the point (0, 0).
SOLUTION: Let x and y are the cost of a DVD and a book.
Multiply the first and the second equation by 3 and –
4 respectively then add.
Shade the region that includes (0, 0).
The graph of the inequality
is:
Substitute 15 for y in the first equation and solve for
x.
ANSWER: The cost of a DVD is $20.
The cost of a book is $15.
ANSWER: DVD: $20; book: $15
Graph each inequality.
76. 75. SOLUTION: The boundary of the graph is the graph of y = 4x – 3.
Since the inequality symbol is , the line will be solid.
Test the point (0, 0).
SOLUTION: The boundary of the graph is the graph of 2x – 3y =
6. Since the inequality symbol is <, the line will be
dashed.
Test the point (0, 0).
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Shade the region that contains (0, 0).
4-5 Completing
the Square
76. 77. SOLUTION: The boundary of the graph is the graph of 2x – 3y =
6. Since the inequality symbol is <, the line will be
dashed.
Test the point (0, 0).
SOLUTION: The boundary of the graph is the graph of
. Since the inequality symbol is
line will be solid.
, the
Test the point (0, 0).
Shade the region that contains (0, 0).
The graph of the inequality is:
Shade the region that does not contain (0, 0).
The graph of the inequality is:
ANSWER: ANSWER: 77. SOLUTION: The boundary of the graph is the graph of
. Since the inequality symbol is
line will be solid.
Write the piecewise function shown in each
graph.
, the
Test the point (0, 0).
78. eSolutions Manual - Powered by Cognero
Shade the region that does not contain (0, 0).
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SOLUTION: The left portion is the graph of the constant function f
(x) = –4. There is a dot at –2, so the constant
4-5 Completing the Square
Write the piecewise function shown in each
graph.
79. 78. SOLUTION: The left portion is the graph of the constant function f
(x) = –8. There is a dot at –2, so the constant
function is defined for x ≤ –2.
The center portion is the graph of f (x) = 2x – 6.
There is circle at –2 and a dot at 5, so the function is
defined for –2 < x ≤ 5.
The right portion is the graph of f (x) = 2x – 18. There is a circle at –5, so the function is defined for
> 5.
The piece-wise function is:
SOLUTION: The left portion is the graph of the constant function f
(x) = –4. There is a dot at –2, so the constant
function is defined for x ≤ –2.
The center portion is the graph of f (x) = –2x + 3.
There are circles at –2 and 1, so the function is
defined for –2 < x < 1.
The right portion is the graph of f (x) = x – 5. There is
a dot at 2, so the function is defined for x ≥ 2.
The piece-wise function is:
ANSWER: ANSWER: 80. 79. SOLUTION: The left portion is the graph of the constant function f
eSolutions
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Cognero
(x) =Manual
is abydot
at –2, so the constant
–8. There
function is defined for x ≤ –2.
SOLUTION: The left portion is the graph of f (x) = x + 12. There is
dot at –6, so the function is defined for x ≤ –6.
The center portion is the graph of the constant
function f (x) = 8. There are circles at –6 and 2,Page
so 28
the constant function is defined for –6 < x < 2.
The right portion is the graph of f (x) = –2.5x + 15.
4-5 Completing the Square
ANSWER: –4
82. a = –2, b = –7, c = 3
SOLUTION: Substitute a = –2, b = –7, and c = 3.
80. SOLUTION: The left portion is the graph of f (x) = x + 12. There is
dot at –6, so the function is defined for x ≤ –6.
The center portion is the graph of the constant
function f (x) = 8. There are circles at –6 and 2, so
the constant function is defined for –6 < x < 2.
The right portion is the graph of f (x) = –2.5x + 15.
There is a dot at 2, so the function is defined for x ≥ 2.
The piece-wise function is:
ANSWER: 73
83. a = –5, b = –8, c = –10
SOLUTION: Substitute a = –5, b = –8, and c = –10.
ANSWER: ANSWER: –136
2
Evaluate b – 4ac for the given values of a, b,
and c.
81. a = 5, b = 6, c = 2
SOLUTION: Substitute a = 5, b = 6, and c = 2.
ANSWER: –4
82. a = –2, b = –7, c = 3
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SOLUTION: Substitute a = –2, b = –7, and c = 3.
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