Name
Name
L E SSON
M AST E R
L E SSON
M AST E R
Questions on SPUR Objectives
6-1
A
See pages 413-415 for objectives.
Skills Objective A
In 1–6, expand and simplify.
1. (x 1 11)2
x 2 1 22 x 1 121
)
1 2
2
4. (5y 2 8)2
36n 22 6n 1 14]
p52
6. -7(8z 1 12)2
-448z 221344z 2 1008
20c
8. Determine the area of the shaded
region if x 5 3 cm.
111 cm2
x+7
3. r 2 5 16
n52
r 5 64
5. n 2 3 5 8
4. 2s 1 7 5 10
n 5 11 or n 5 -5
all real numbers
-4
x+9
8. Simplify - =(2 2 6)2 .
2x – 3
9. Describe how the graphs of y 5 =x 2 and
y 5 - x are related.
Sample: Both graphs contain (0, 0); the graphs
are reflections of each other over the x-axis.
x
Uses Objective G
Uses Objective G
9. Cindy has an 110 by 140 photograph that she wishes to
frame. She wants matting of width w around the edge
of the photograph.
a. Give an expression for the total area of
4w 2 1 50w 1 154 in 2
the photograph and the matting.
b. If w 5 2 in., what are the inner dimensions
of the frame that will hold the photograph and
15 in.; 18 in.
the matting?
c. What is the total area of the photograph and
270 in 2
the matting in Part b?
=72π , or
10. A rectangle measures 6 in. by 12 in.
What is the radius of a circle which has
the same area as the rectangle?
Representations Objective J
In 11 and 12, graph the equation.
11. y 5 x 1 3
y
5
5
5
x
-5
Name
58
Name
L E SSON
M AST E R
L E SSON
M AST E R
Questions on SPUR Objectives
6-3
A
See pages 413-415 for objectives.
Uses Objective I
20x 143
a. Write an equation for its image.
y 1 7 5 -5(x 2 3)2
(4, -12)
b. (1, -5) is a point on the preimage. What is
the corresponding point on the image?
4. Suppose a ball is thrown upward from a height of 5 feet
with an initial velocity of 30 ft/sec.
a. Write an equation relating the time t in
seconds and the height h of the ball in feet.
In 3 and 4, assume parabola P is
a translation image of parabola Q.
8
-8 -6 -4
2
4
6
a. Write an equation that describes
the relationship between h, the
height in feet of the ball above
the ground, and time t
in seconds.
h 5 -16t 2 179
x
-4
4. Parabola P has equation y 5 -2x2.
Write an equation for parabola Q.
P
-8
y 2 12 5 -2(x 1 5)2
-12
b. On the grid at the right, graph the
height h after t seconds.
In 6–8, an equation for a parabola is given. a. Graph the
parabola and show its axis of symmetry. b. Identify its
vertex. c. Write an equation for the axis of symmetry.
6. y 5 3(x 1 1)
7. y 1 4 5 -3x
a.
5
10x
-10
-5
c.
a.
10
5x
b.
c.
y
b.
c.
2
6. Johanna threw a water balloon upward at a speed of 10m/sec
while standing on the roof of a building 12 meters high.
a. What was the height of the balloon after
12.4
2 seconds?
-15
(0, -4)
x50
1
3
t
Sample: About 2.2 seconds; this is the
approximate value of t when h 5 0.
15
15x
-15
-10
(-1, 0)
x 5 -1
0
2
y
h
100
80
60
40
20
c. Estimate how long it would take the ball to reach the
ground. Explain your reasoning.
8. y 2 5 5 (x 1 3)
2
h 5 -16t 2 130t 15
14 ft
5. Suppose a ball is dropped from the top of a 79-foot-tall tree.
4
T-5, 12
ADVANCED ALGEBRA © Scott, Foresman and Company
b. Find the height of the ball after 1.5 seconds.
y
12
Q
3. What translation maps parabola P
onto parabola Q?
4
x 14
Uses Objective G
Representations Objective J
2
24x 277
1
3. y 2 3 5 4 (x 2 2)2
y 5 1] x 2 2
ADVANCED ALGEBRA © Scott, Foresman and Company
b. Name the vertex of the image.
2. The graph of y 5 -5x2 is translated 3 units to the right and 7 units down.
-5
See pages 413-415 for objectives.
In 1–3, write the equation in standard form.
2. y 1 5 5 -2(x 2 6)2
1. y 5 2(x 1 5)2 2 7
y 5 2x 2 1
y 5 -2x 2 1
y 2 6 5 (x 1 12)2
(-12, 6)
a. Write an equation for its image.
y
Questions on SPUR Objectives
6-4
A
Skills Objective B
1. The graph of y 5 x2 is translated 12 units to the left and 6 units up.
b.
x
5
-5
-5
57
4.79, in.
12. y 1 2 5 - x
y
-5
a.
s 5 1.5 or
s 5 -8.5
Properties Objective E
7. For what real numbers does x 5 -x?
In 7 and 8, use the rectangles pictured at the right.
7. Write an expression for the area of
the shaded region.
-x 2 1 19x 1 63
ADVANCED ALGEBRA © Scott, Foresman and Company
4. (2p 2 4)2 5 0
25y 2 2 80y 1 64
5. (c 1 5)2 2 (c 2 5)2
2. (n 2 2)2 5 0
m 5 6 =20
6 4.47
3d 21 12d 1 12
See pages 413-415 for objectives.
ADVANCED ALGEBRA © Scott, Foresman and Company
(
3. 6n 2
2.
Skills Objective C
In 1–4, solve.
1. m2 5 20
1
2
3 (3d 1 6)
Questions on SPUR Objectives
6-2
A
(-3, 5)
x 5 -3
b. Assume that the balloon did not land on the
roof, and estimate how long it took the
balloon to reach the ground.
59
m
2.9 sec
60
©
155
Name
LESSON
MASTER
L E S S O N M A S T E R 6-4 A page 2
y
5
15
5
x
-5
-5
5
Skills Objective B
In 2–5, write the equation in vertex form.
2. y 5 x2 2 6x 1 10
3. y 5 x2 1 14x 1 5
x
y 2 1 5 (x 2 3)2
y 1 44 5 (x 1 7)2
4. y 5 5x2 2 15x 2 4
3
}
] )2
y 1 61
4 5 5(x 2 2
5. 6y 5 3x2 1 30x 1 25
1] (x 1 5) 2
}
y 1 25
3 52
In 6 and 7, find the vertex of the parabola
determined by the equation.
6. y 5 x2 2 12x 1 24
7. y 5 -4x2 1 6x 2 7
Height (ft)
50
b. When did the ball reach its
maximum height?
40
})
( 3]4, - 19
4
(6, -12)
30
20
10
1.8 sec
1
2 3 4
Time (sec)
5
t
In 8 and 9, write an equation in vertex form
equivalent to the standard equation given.
9. y 5 10x2 1 10x 1 1
8. y 5 2x2 2 20x 1 57
y 1 23] 5 10(x 1 12] ) 2
y 2 7 5 2(x 2 5)2
52 ft
c. What was the maximum height?
d. When was the ball 30 ft in
the air?
0.3 sec and 3.2 sec
Answers to Question 9 may vary slightly.
10. Multiple choice. Which equation is equivalent to
y 5 18x2 1 60x 1 45?
(a) y 1 3 5 2(3x 1 3)2
(c) y 1 5 5 2(3x 2 5)2
b
(b) y 1 5 5 2(3x 1 5)2
(d) y 2 5 5 2(3x 1 5)2
11. True or false. y 5 4x2 1 4x 2 6 and
true
1
y 1 7 5 4(x 1 2 )2 have the same vertex.
61
Name
62
Name
LESSON
MASTER
6-6
A
LESSON
MASTER
Questions on SPUR Objectives
See pages 413-415 for objectives.
Uses Objective H
6-7
A
Questions on SPUR Objectives
See pages 413-415 for objectives.
Skills Objective C
In 1–6, use the Quadratic Formula to solve the equation.
1. The following pictures illustrate the first five numbers
in a sequence we shall call the “rectangular numbers.”
1. x2 1 6x 2 7 5 0
2. 7 5 3x2 2 4x
x 5 3]7 or x 5 -1
x 5 1 or x 5 -7
3. m(m 1 6) 5 36
2
6
12
20
m5
30
a. Draw the next rectangular number
above at the right.
b. Find the next three rectangular numbers
after 30.
or
42, 56, 72
R (n ) 5 n 2 1 n
c. Give a formula for R(n), the nth
rectangular number.
d. Use your formula to find the 100th
rectangular number.
Years of Service y
2
4
8
12
16
20
26
5 1 =37
2
5.54
or
5 1 =37
2
-.54
6. (3a 1 2)(5a 2 1) 5 2(5a 2 1)
a 5 0 or a 5 15]
4 ft
a. How high was the ball when Juan hit it?
b. How far from the plate, along the ground,
was the ball when it was the same height
416 23]
at which Juan hit it?
c. How far from the plate, along the ground,
42.8 ft ,
was the ball when it was 100 feet high?
d. The fence is 405 feet away from home plate, and it
is 12 feet high. Did the ball go over the fence?
Explain your reasoning.
ft
373.9 ft
Yes; when the ball was 405 feet from home
plate, it was about 32 feet above the ground.
5000
c. Fit a linear model to these
data and plot it.
y
8. A toy rocket was shot straight up with an initial velocity of
75 m/sec. The platform from which the rocket was shot is
2.3 meters high.
a. When was the rocket 100 meters above
the ground?
Sample answers are given for 2b–2d.
b. When did the rocket hit the ground?
63
156
w5
7. Juan Torres hit a fast ball thrown by Liz Buckner. Let
x be the distance on the ground in feet of the ball from
home plate and h(x) be the height in feet of the ball at
that distance. Suppose the path of the ball is described
by the function h(x) 5 -.006x 2 1 2.5x 1 4.
s
0 4 8 12 16 20 24 28
$7170 or
d. Use either model to estimate the monthly salary
$7649
of a U.S. general with 10 years of service.
-9.71
3
}
d 5 10
or d 5 - 45]
10,000
b. Fit a quadratic model to
these data and plot it.
2
s51.3y 162.5y16415
s 5 95y 16699
4. w 2 5 5w 1 3
3.71
Uses Objective G
Monthly Salary s
$6,889.20
$6,889.20
$7,153.50
$7,549.80
$8,089.80
$8,631.60
$9,169.50
a. On the grid at the right, make
a scatterplot of these data.
- 6 1= 180
2
- 6 2= 180
2
5. 50d 2 2 12 5 -25d
10,100
2. The following table gives the monthly salaries in 1993
for U.S. generals having various years of service.
ADVANCED ALGEBRA © Scott, Foresman and Company
16
h
5 ft
ADVANCED ALGEBRA © Scott, Foresman and Company
1. Fill in the blank to make a perfect square.
?
4d 2 2 16d 1
-15
9. On the graph at the right, the height of
a baseball hit upward is shown as a
function of time.
a. What was the initial height of
the ball?
See pages 413-415 for objectives.
ADVANCED ALGEBRA © Scott, Foresman and Company
-5
Questions on SPUR Objectives
Vocabulary
Representations Objective J
In 7 and 8, graph the parabola for -3 ≤ x ≤ 3.
7. y 5 x 2 1 x 2 6
8. y 5 -2x2 1 5x 1 7
y
6-5
A
64
1.4 sec, 13.9 sec
15.3 sec
ADVANCED ALGEBRA © Scott, Foresman and Company
©
Name
Name
Name
L E SSON
M AST E R
6-8
A
L E SSON
M AST E R
Questions on SPUR Objectives
See pages 413-415 for objectives.
Questions on SPUR Objectives
See pages 413-415 for objectives.
V ocabulary
Skills Objective C
3
1. In =6 1 2 i, name the real part
and the imaginary part. real
1. Show that i =65 is a square root of -65.
(i =65 ) 5 i ( =65 ) 5 -1(65) 5 -65
2
2
In 2–5, true or false.
Skills Objective D
In 2 and 3, simplify.
2. (5i 2 3i)(5i 1 3i)
false
false
false
true
2. The solution to x 5 -5 are =5 and - =5 .
2
3. The solution to g2 5 -13 are 13i and -13i.
4. i =31 5 -i =31
5. i =17 is a square root of -17.
=6
3. (5i 1 3i) 1 (5i 2 3i)
10i
-16
In 4–13, perform the operations and give the answer
in a 1 bi form.
4. (6 2 i) 1 (3 1 4i)
5. (6 2 i)2(3 1 4i)
9 1 3i
In 6–7, solve.
6. 9r 2 1 13 5 -12
7. (s 1 2) (s 2 2) 5 -8.
r 5 53]i or r 5 -53]i
3 2 5i
7.
8. 5(3 2 2i)
9. (4 1 2i)(-3 2 i)
2
15 2 10i
5
-12
9. 3i • 4i
10. -5(3 2 i)
11.
-15 1 5i
11. =15 • =-15
12. =-3 =-3
13. =-25 1 =-64
13i
14. -2 =-4
-4i
15. 12i 2 18i
-6i
1
]2
In 14–19, suppose m 5 1 1 8i and n 5 -2 1 3i.
Evaluate and write the answer in a 1 bi form.
17. (i =12 )2
-12
14. mn
=-9
=-36
18. 3i(4i 1 5i)
12. 8 6 =-36
2
-27
4i
15. n 2
-26 2 13i
Name
17. 4m 1 3n
18. im 2 in
19. m2 1 2m 1 1
-2 1 41i
6-10
A
66
L E SSON
M AST E R
Questions on SPUR Objectives
See pages 413-415 for objectives.
Skills Objective C
Questions on SPUR Objectives
See pages 473-475 for objectives.
2. 3x 5 7 1 5x2
7
x 5 4 6 =71
i
4
3 =131
x5 10
6 10 i
3. -4(2n2 2 2n) 5 3(n 1 6)
=551
5
n5 16
6 16
i
Properties Objective F
In 4 and 5, a quadratic equation is given. a. Evaluate
its discriminant. b. Give the number of real solutions.
c. Tell whether the real solutions are rational or irrational.
4. 15x2 2 3x 1 7 5 0
a.
b.
c.
In 6–9, give the number of real solutions.
2
0
6. 5z 5 12z2 2 5
8. 6c2 2 c 1 15 5 0
c.
9. 9 2 12t 5 t 2 2 3
Uses Objective F
4
4. In a game with a friend, Felipe has a 7 chance of
winning a round, and each round is independent.
Suppose Felipe and his friend play six rounds. What
is the probability that Felipe will win all six rounds?
2
2
.0348
5. Multiple choice. Which of the following could be a
graph of an odd power function?
(a)
In 10 and 11, give the number of x-intercepts
of the graph of the parabola.
11. y 1 14 5 -3(x 2 2)2
( 47] )6
Representations Objective I
Representations Objective K
0
.
No; a power function is of the form
g (x) 5 x n, where n is a positive integer.
961
2 solutions
rational
7. 19w2 5 7w
base
x
.
?
2. The identity function f has the equation f (x) 5
1
3. If g(x) 5 x , is g an example of a power function?
Why or why not?
5. 15h2 2 11h 2 14 5 0
- 411
0 solutions
?
1. In the expression b n, b is called the
(b)
y
x
0
12. Does the parabola with equation y 5 - 14 x2 1 x 2 3 ever intersect the
line with eqution y 5 -2? If so, how
many points of intersection are
there? Explain your reasoning.
Yes; one; the equation -2 5 - 1 x 2 1 x 2 3
b
(c)
y
y
x
x
6. The point (-2, -32) is on the graph of an odd power function.
a. What other point must be on the graph?
has
4
x 5 2 as its only solution, so the parabola and
the line intersect at the single point (2, -2).
b. Write an equation for this function.
(2, 32)
y 5 x5
y
7. a. On the grid at the right, sketch graphs
of f(x) 5 x 3 and g(x) 5 x 5.
1
b. For what values(s) of x is f(x) 5 g(x)?
x 5 -1, 0, 1
13. The graph of y 5 4x2 has one x-intercept. How many x-intercepts does
the graph of y 5 4(x 2 h)2 have if h Þ 0? Explain your reasoning.
One; the graph of y 5 4(x 2 h)2 will be a
c. For what values of x is f(x) > g(x)?
x < -1, 0 < x < 1
horizontal translation image of the graph
of y 5 4x 2.
1
-1
-1
67
g (x) f (x)
68
157
x
ADVANCED ALGEBRA © Scott, Foresman and Company
1. 2x2 2 7x 1 15 5 0
10. y 5 15x2 1 7
7-1
A
V ocabulary
In 1–3, solve.
b.
-60 1 32i
Name
L E SSON
M AST E R
a.
-5 2 12i
16. 4m 1 3
7 1 32i
65
11i
2
13. ( =2 1 i =2 )2
4 6 3i
-5 1 3i
ADVANCED ALGEBRA © Scott, Foresman and Company
21i
32i
-3
16.
12i
-10 2 10i
15i
10. =-361
19i
2
11i
6. (1 1 i)(1 2 i)
s 5 2i or s 5 -2i
Skills Objective D
In 8–18, simplify.
8. -5i 2
3]
2
imaginary
ADVANCED ALGEBRA © Scott, Foresman and Company
2
ADVANCED ALGEBRA © Scott, Foresman and Company
6-9
A