Name————————————————————————
Lesson
2.8
Date —————————————
Practice B
For use with the lesson “Analyze Graphs of Polynomial Functions”
If 26 is a solution of the polynomial equation f (x) 5 0, then 26 is a factor of f(x).
State the maximum number of turns in the graph of the function.
2. f(x) 5 x 4 1 2x 2 1 4
3. f (x) 5 23x 3 1 x 2 2 x 1 5
4. g(x) 5 2x 6 1 1
5. g(x) 5 4x 2 2 5x 1 3
6. h(x) 5 3x 7 2 6x 2 1 7
7. h(x) 5 2x 9 2 8x 7 1 7x 5
Lesson 2.8
1. Describe and correct the error in the following statement.
Determine the x-intercepts of the function.
8. g(x) 5 (x 1 3)(x 2 2)(x 2 5)
9. h(x) 5 (x 1 4)(x 2 6)(x 2 8)
10. f(x) 5 (x 1 3)2(x 2 2)
11. f (x) 5 (x 1 5)(x 1 1)(x 2 7)
12. g(x) 5 (x 1 6)3(x 1 2)
13. h(x) 5 (x 2 8)5
Graph the function.
14. f(x) 5 (x 2 3)(x 1 2)(x 1 1)
15. g(x) 5 (x 2 3)2(x 1 2)
y
y
5
Copyright © Houghton Mifflin Harcourt Publishing Company. All rights reserved.
2
x
3
x
1
16. h(x) 5 0.3(x 1 6)(x 2 1)(x 2 4)
y
5
17. g(x) 5 ​ }​ (x 1 1)2(x 2 1)(x 2 4)
6
5
y
x
1
5
2
x
18. h(x) 5 (x 2 1)(x 2 1 x 1 1)
19. f (x) 5 (x 1 2)(x 2 1 2x 1 2)
y
y
1
1
x
1
1
x
Algebra 2
Chapter Resource Book
2-89
Name————————————————————————
Lesson
Lesson 2.8
2.8
Date —————————————
Practice B
continued
For use with the lesson “Analyze Graphs of Polynomial Functions”
Estimate the coordinates of each turning point and state whether each
corresponds to a local maximum or a local minimum. Then estimate all
real zeros and determine the least degree the function can have.
y
20.
y
21.
y
22.
1
1
x
1
1
x
1
1
x
Use a graphing calculator to graph the function. Identify the x-intercepts
and points where local maximums or local minimums occur.
23. f(x) 5 3x 3 2 9x 1 1
1
2
24. h(x) 5 2​ }​ x 3 1 x 2 }
​ 3 ​
3
1
25. g(x) 5 2​ }​ x 4 1 2x2
4
26. f (x) 5 x 5 2 6x 3 1 9x
27. h(x) 5 x 5 2 5x 3 1 4x
28. g(x) 5 x 4 2 2x 3 2 3x 2 1 5x 1 2
29. Food The average number E of eggs eaten per person
each year in the United States from 1970 to 2000 can be
4
3
2
E 5 0.000944t 2 0.052t 1 0.95t 2 9.4t 1 308
where t is the number of years since 1970. Graph
the function and identify any turning points on the
interval 0 ≤ t ≤ 30. What real-life meaning do these
points have?
Per capita eggs
modeled by
E
325
300
275
250
225
200
0
0 5 10 15 20 25 30 35 t
Years since 1970
30. Quonset Huts A Quonset hut is a dwelling shaped like half a cylinder. You have
600 square feet of material with which to build a Quonset hut.
a. The formula for surface area is S 5 πr 2 1 πrl where r is the radius of the
semicircle and l is the length of the hut. Substitute 600 for S and solve for l.
1
b. The formula for the volume of the hut is V 5 }
​ 2​πr 2l. Write an equation for the
volume V of the Quonset hut as a polynomial function of r by substituting the
expression for l from part (a) into the volume formula.
c. Use the function from part (b) to find the maximum volume of a Quonset hut
with a surface area of 600 square feet. What are the hut’s dimensions?
2-90
Algebra 2
Chapter Resource Book
Copyright © Houghton Mifflin Harcourt Publishing Company. All rights reserved.
Per Capita Egg
Consumption
Lesson 2.7 Apply the
Fundamental Theorem of
Algebra, continued
y
19.
y
2
x
22
Lesson 2.8 Analyze Graphs of
Polynomial Functions
Teaching Guide
21.
y
y
22.
1
3. (21.7, 10.4) and (1.7, 210.4)
Graphing Calculator Activity
1. local maximum: (0.37, 13.51); local minima:
(21.83, 212.66), (2.96, 227.04)
2. local maximum: (22.54, 0.88); local
minimum: (20.13, 26.06) 3. local maximum:
(0, 36); local minima: (22.55, 26.25),
(2.55, 26.25) 4. local maximum (22.67, 29.63);
local minimum: (2.0, 272) 5. local maxima:
(21.57, 1.92), (2.25, 8.63); local minimum:
(0.07, 24.02) 6. local maximum: (24.19, 16.16);
local minimum: (2.86, 254.08)
Practice Level A
1
x
1
23. a. 4 b. 4 c. (22, 0), (6, 0) 24. a. 0 < x < 9,
because the sides must be less than 9 inches.
b. 3 in. c. 432 in.3
1. The error is in calling 26 a factor. The correct
statement is If 26 is a solution of the polynomial
equation f(x) 5 0, then (x 1 6) is a factor of f(x).
2. 3 3. 2 4. 5 5. 1 6. 6 7. 8 8. 23, 2, 5
9. 24, 6, 8 10. 23, 2 11. 25, 21, 7
12. 26, 22 13. 8
y
14.
y
15.
5
x
2
3
x
1
y
16.
17.
y
5
1. False. Sample answer: If k is an imaginary
zero, then it is not an x-intercept of the graph of
f(x). 2. 4 3. 5 4. 3 5. (21.5, 5.5): max,
(0.5. 3): min 6. (1, 2): min 7. (21.5, 23.75):
min, (0.5, 1.25): max, (1, 1): min 8. B 9. C
10. A 11. 24; 1 12. 2; 3 13. 24; 0; 5
14. 23, 21, 8 15. 26 16. 1; 7
y
18.
1
x
2
Practice Level B
1. (0, 3) and (2, 21) 2. (1, 29)
17.
answers
polynomial is equal to the opposite of the
coefficient of the x n 2 1 term. c. The product of
the zeros of an nth-degree polynomial is equal to
the constant term if the function is of even degree
and to the opposite of the constant term if the
function is of odd degree. 10. The concentration
is the greatest after about 4.5 hours.
y
4 x
22
b. The sum of the zeros of an nth-degree
Copyright © Houghton Mifflin Harcourt Publishing Company. All rights reserved.
20.
2
x
1
x
5
6 x
y
18.
y
19.
1
2
1
x
1
1
x
1
x
20. (20.5, 0.5): max, (0.5, 20.3): min; 20.6, 0,
0.6; 3 21. (22, 0): min, (20.5, 5): max, (1, 0):
min; 22, 1; 4 22. (22.8, 1.9): max, (0, 0.25):
min, (2, 1): max; 23.8, 2.8; 4 23. x-int: 21.79,
0.11, 1.67; max: (21, 7); min: (1, 25)
1
2
4
24. x-int: 22, 1; max: (1, 0); min: ​ 21,2​ }​  ​
3
Algebra 2
Chapter Resource Book
A31
8.
y
10
(21.73, 0), (0.77, 4.46); min: (20.77, 24.46),
(1.73, 0) 27. x-int: 22, 21, 0, 1, 2; max:
(21.64, 3.63), (0.54, 1.42); min: (20.54, 21.42),
(1.64, 23.63) 28. x-int: 21.53, 20.35, 1.88, 2;
max: (0.61, 3.62); min: (21.05, 23.03),
(1.94, 20.03)
x
1
6
25. x-int: 22.83, 0, 2.83; max: (22, 4), (2, 4);
min: (0, 0) 26. x-int: 21.73, 0, 1.73; max:
29.
9.
y
x
1
domain: 2` < x < `
range: 2` < y < `
domain: 2` < x < `
range: 2` < y < `
10.
11.
4
y
y
28
x
1
240
x
Per capita eggs
Per Capita Egg
Consumption
E
325
300
275
250
225
200
0
0 5 10 15 20 25 30 35 t
Years since 1970
(25.33, 222.93); Sample answer: From 1970 to
1995, per capita egg consumption decreased to
about 223 eggs, then began to increase again.
600
30. a. l 5 }
​ πr ​2 r b. V 5 300r 2 0.5πr 3
c. 1596 ft3; r < 7.98 ft, l < 15.95 ft
Practice Level C
1. 3 2. 2 3. 4
4.
5.
y
y
1
2
domain: 2` < x < ` domain: 2` < x < `
range: y ≥ 222.9
range: 2` < y < `
12. (22, 2.4): max, (0, 21.2): min, (1, 21): max,
(2.1, 22): min; 22.5, 21, 2.7; 5 13. (22, 21):
max, (0, 22.2): min, (1, 22): max; none; 4
14. (21.5, 22.25): min, (0, 3): max, (2, 23):
min, (3.5, 2): max; 22, 21, 1, 3, 4; 5
15. x-int: 20.34, 1.43, 2.1; max: (0.7, 2.44);
min: (1.83, 21.55) 16. x-int: 0, 1.2; max:
(21.19, 4.09); min: (21.77, 3.8), (0.71, 22.93)
17. x-int: 20.88, 1.08, 1.41; max: (1.26, 0.08);
min: (0, 20.88) 18. x-int: 25, 0, 1.2; max:
(0.42, 1.38); min: (23.57, 2116.16), (1.2, 0)
19. 21 20. 2, 4 21. 1, 3, 5
22. If n is even, there is a turning point. If n is
odd, the graph passes through the x-axis.;
x
1
y
x
1
y
1
1
1
domain: 2` < x < `
range: 2` < y < `
6.
domain: 2` < x < `
range: 2` < y < `
7.
y
x
x
500 2 πr 2
23. a. h 5 }
​  πr ​
y
1
2
1
x
1
1
x
1
b. V 5 500r 2 }
​ 3 ​ π r 3
c. about 3613.79 ft3; r < 10.84 ft, h < 2.56 ft
domain: 2` < x < `
range: y ≥ 24.489
A32
Algebra 2
Chapter Resource Book
domain: 2` < x < `
range: y ≤ 0.8
Study Guide
1.
; x-intercepts: (22, 0),
(4, 0);
maximum: (22, 0),
minimum: (2, 216)
Copyright © Houghton Mifflin Harcourt Publishing Company. All rights reserved.
answers
Lesson 2.8 Analyze Graphs
of Polynomial Functions,
continued