LESSON
2.8
Answers for the lesson “Analyze Graphs of
Polynomial Functions”
Skill Practice
y
6.
1. turning
1
21
2. Sample answer: A local
maximum occurs at a turning
point on the graph of a function
and is higher than any nearby
point, but it may not be the
highest point on the graph.
y
7.
y
3.
x
1
23
x
1
22
x
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4.
y
4
8.
21
y
x
3
y
5.
21
x
y
9.
2
24
x
1
21
x
Algebra 2
Answer Transparencies for Checking Homework
77
10.
14. The function is a fourth degree
y
2
21
x
polynomial with a positive
leading coefficient, so its end
behavior should be to positive
infinity at both ends.
y
y
11.
1
21
21
x
x
15-20. Sample answers are given.
y
12.
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1
2
21
x
15. local maximum: (20.3, 0.3),
local minimum: (0.9, 21.3);
zeros: 20.75, 0, 1.4,
least degree: 3
16. local maximum: (20.5, 22.4),
local minimum: (1.5, 25.7);
zero: 2.7, least degree: 3
13. The x-intercepts should be
at 22 and 1.
17. local maximums: (1, 0), (3, 0),
local minimum: (2, 22);
zeros: 1, 3, least degree: 4
y
18. local maximum: (20.25, 22),
local minimums: (21.5, 25),
(0.5, 22.4);
zeros: 22, 1, least degree: 4
1
21
x
Algebra 2
Answer Transparencies for Checking Homework
78
19. local maximums: (21.1, 0.8),
(1.9, 8),
local minimums: (22.2, 238),
(0.3, 240), (2.8, 213);
zeros: 22.6, 21.2, 21, 1.5,
2.2, 3, least degree: 6
20. local maximum: (20.5, 20.5),
local minimums: (21.7, 22),
(0.6, 22);
zeros: 22.1, 1.1, least degree: 4
21. B
22. x-intercepts: 23.9, 20.67, 0.57;
local maximum: (22.7, 16);
local minimum: (0, 23)
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23. x-intercept: 22.5;
local maximum: (21.2, 4.0);
local minimum: (1.2, 0.96)
24. x-intercepts: 0, 1.4;
local maximum: (0.91, 2.0);
local minimum: none
25. x-intercepts: 22.2, 1, 1.7;
local maximums: (21.6, 10.5),
(0.17, 2.0);
local minimums: (0, 2),
(1.5, 21.7)
26. x-intercepts: 21.9, 0, 1.5;
local maximum: (0.17, 0.08);
local minimums: (21.3 23.5),
(1.1, 21.1)
27. x-intercepts: 20.77, 4.5;
local maximum: (0.47, 22.6);
local minimums: (20.16, 23.1),
(3.4, 239.4)
28. x-intercepts: 22.1, 20.23, 2.0;
local maximum: (21.5, 18.4);
local minimum: (1.2, 219.1)
29. x-intercepts: 20.77, 0, 0.82;
local maximum: (0.47, 1.6);
local minimum: (20.46, 21.5)
30. D
31. Sample answer: Quadratic
functions only have one turning
point, therefore one maximum or
minimum value. Cubic functions
can have two turning points,
therefore one maximum and one
minimum, and the end behavior
is to positive and negative infinity,
so there is no overall maximum or
minimum value.
32. Sometimes. Sample answer:
y 5 x 3 1 10x does not have a
turning point, but more of a bend
in the graph.
33. Check student’s work. Sample
answer: for exercise 22 (intervals
are approximate): negative:
x , 23.90, 20.67 , x , 0.57;
positive: 23.90 , x , 20.67,
x . 0.57; increasing: x , 22.67,
x . 0; decreasing: 22.67 , x , 0
Algebra 2
Answer Transparencies for Checking Homework
79
34.
5
1
21
1
x
domain: all real numbers,
range: all real numbers
y
35.
y
37.
y
x
domain: all real numbers,
range: yq221.3
38. Odd-degree: domain and range
5
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21
x
domain: all real numbers,
range: all real numbers
36.
will both always be all real
numbers; even-degree: domain
will always be all real numbers,
range will either be all numbers
greater than or equal to the
minimum value or all numbers
less than or equal to the
maximum value.
Problem Solving
y
39. maximum: about 5.8 in.
1
21
x
by 13.8 in. by 2.1 in.;
about 168 in.3
40. maximum: about 18.6 cm
domain: all real numbers,
range: yq21.7
by 28.6 cm by 5.7 cm;
about 3032 cm3
Algebra 2
Answer Transparencies for Checking Homework
80
43. a.
S
4
S
50,000
Enrollment (thousands)
Speed (meters per second)
41.
3
2
1
0
0
1
Seconds
2 t
40,000
30,000
20,000
10,000
0
0
8
16
24
32
Years since 1960
after about 0.95 sec
600 2 :r 2
42. a. }
:r
b. local max: (11.7, 44,971),
local min: (29.8, 40,078);
Sample answer: The local
maximum indicates that in
1972 the number of students
enrolled was about 44,971,000.
The local minimum indicates
that in 1990 there were about
40,078,000 students enrolled.
1
b. V 5 300r 2}:r3
2
V
1600
Volume (ft 3)
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c.
1200
800
c. 36,300aSa47,978
400
0
40 x
1
2
h2
44. V(h) 5 h: 64 2 } ; about 9.2;
4
0
4
8
12
16
Radius (feet)
r
about 1238
r 5 about 8 ft,
* 5 about 15.9 ft;
about 1595.77 ft 3
Algebra 2
Answer Transparencies for Checking Homework
81
Mixed Review of
Problem Solving
3. 1995;
1
9
9
5
1. a. x 3 1 6x 2 1 5x 2 180 5 0
b. 61, 62, 63, 64, 65, 66,
69, 610, 612, 615, 618,
620, 630, 636, 645, 660,
690, 6180
c. 4; after dividing by (x 2 4)
the quotient is x 2 1 10x 1 45,
which has no real zeros.
d. 9 in. by 5 in. by 4 in.
2. a. V 5 x(20 2 2x)(30 2 2x)
4. x 4 2 7x 3 1 7x 2 1 33x 2 34
b.
5. Sample answer:
y 5 x 4 1 3x 2 1 24
V
Volume (in.3)
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960
6. a.
x 4
720
480
x
240
0
x
0
2
4
6
8
Side length of square
cutouts (in.)
10 x
1
b. V 5 }(x 3 2 4x 2)
3
c. about 12.2 in. by 22.2 in.
by 3.9 in.
d. about 1056 in.3
Algebra 1
Answer Transparencies for Checking Homework
82
c.
V
Volume (in.3)
800
600
400
200
0
0
4
8
12
16
x
Length of base (in.)
10
1
d. 200 5 }(x 3 2 4x 2);10;
3
the answers are the same;
base sides: 10 in., height: 6 in.
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7. t3 2 3t2 1 6; $202
8. y 5 20.000324x 3 1 0.0542x 2 2
1.71x 1 13.9
Algebra 1
Answer Transparencies for Checking Homework
83