Algebra 2 Final Exam Review
Multiple Choice
Identify the choice that best completes the statement or answers the question.
1. Add. Write your answer in standard form.
a.
b.
c.
d.
2. A florist delivers flowers to anywhere in town. d is the distance from the delivery address to the florist
shop in miles. The cost to deliver flowers, based on the distance d, is given by
. Evaluate
for
and
, and describe what the values of
the function represent.
a.
;
.
represents the cost, $15.24, of delivering flowers to a destination that is 6 miles from
the shop.
represents the cost, $22.09, of delivering flowers to a destination that is 11 miles
from the shop.
b.
;
.
represents the cost, $62.04, of delivering flowers to a destination that is 6 miles from
the shop.
represents the cost, $179.39, of delivering flowers to a destination that is 11 miles
from the shop.
c.
;
.
represents the cost, $23.43, of delivering flowers to a destination that is 6 miles from
the shop.
represents the cost, $49.62, of delivering flowers to a destination that is 11 miles
from the shop.
d.
;
.
represents the cost, $22.09, of delivering flowers to a destination that is 6 miles from
the shop.
represents the cost, $15.24, of delivering flowers to a destination that is 11 miles
from the shop.
3. Graph the polynomial function
on a graphing calculator. Describe the
graph, and identify the number of real zeros.
a. From left to right, the graph alternately increases and decreases, changing direction two
times. It crosses the x-axis three times, so there appear to be three real zeros.
b. From left to right, the graph alternately increases and decreases, changing direction three
times. It crosses the x-axis two times, so there appear to be two real zeros.
c. From left to right, the graph alternately increases and decreases, changing direction three
times. It crosses the x-axis four times, so there appear to be four real zeros.
d. From left to right, the graph increases and then decreases. It crosses the x-axis twice, so
there appear to be two real zeros.
4. Find the product
a.
.
c.
b.
d.
5. Ms. Ponce owns a company that makes specialized race car engines. From 1985 through 2005, the
number of engines produced can be modeled by
where is number of years since
1985. The average revenue per engine (in dollars) can be modeled by
polynomial
that can be used to model Ms. Ponce’s total revenue.
a.
b.
c. 36
d.
6. Find the product
a.
b.
. Write a
.
c.
d.
7. Divide by using synthetic division.
a.
c.
b.
d.
8. Determine whether the binomial (
) is a factor of the polynomial
a. Cannot determine.
b. (
) is a factor of the polynomial
.
c. (
) is not a factor of the polynomial
9. Factor
a.
b.
.
.
c.
(
(
)
d.
)
10. Factor the expression
a.
b.
.
.
c.
d.
11. Computer graphics programs often employ a method called cubic splines regression to smooth handdrawn curves. This method involves splitting a hand-drawn curve into regions that can be modeled by
cubic polynomials. A region of a hand-drawn curve is modeled by the function
. Use
the graph of
to identify the values of x for which
and to factor
.
y
5
4
3
2
1
–5
–4
–3
–2
–1
–1
1
2
3
4
5
x
–2
–3
–4
–5
a.
b.
;
;
;
;
c.
;
;
d.
;
;
12. Solve the polynomial equation
a. The roots are 0, –6, and 4.
b. The roots are –18 and 12.
by factoring.
c. The roots are 0, 6, and –4.
d. The roots are –6 and 4.
1
13. Write the simplest polynomial function with zeros 5, –4, and 2 .
a.

3
2
b.

1
2

39
2
 11
x  10
 2 x  10
1
c.
+5
– 4x 
d.


3
2
39
2
1
2
x  10
14. Solve
by finding all roots.
a. The solutions are , ,
, and
.
b. The solutions are , 2, 3i, and i.
c. The solutions are 5 and .
d. The solutions are 5, , 3i, and i.
15. Identify the leading coefficient, degree, and end behavior of the function
a. The leading coefficient is –5. The degree is 4.
As
,
+ 6 and as
+ ,
+6
b. The leading coefficient is –5. The degree is 6.
As
,
– and as
+ ,
–
c. The leading coefficient is –5. The degree is 6.
As
,
+ 6 and as
+ ,
+6
d. The leading coefficient is –5. The degree is 4.
As
,
– and as
+ ,
–
–5
–6
16. Graph
on a calculator, and estimate the local maxima and minima.
a. The local maximum is about 31.627417. The local minimum is about –13.627417.
b. The local maximum is about 13.627417. The local minimum is about –31.627417.
+ 6.
c. The local maximum is about 22.627417. The local minimum is about –22.627417.
d. The local maximum is about –13.627417. The local minimum is about 31.627417.
17. For
a. To graph
, write the rule for
, translate the
left 2 units.
graph of
and sketch its graph.
c. To graph
, translate the
graph of
down 2 units.
y
–10 –8
–6
b. To graph
graph of
–4
y
10
10
8
8
6
6
4
4
2
2
–2
–2
2
4
6
8
10
x
–10 –8
–6
–4
–2
–2
–4
–4
–6
–6
–8
–8
–10
–10
d. To graph
graph of
, translate the
right 2 units.
–6
–4
6
8
10
x
, translate the
y
10
10
8
8
6
6
4
4
2
2
–2
–2
4
up 2 units.
y
–10 –8
2
2
4
6
8
10
x
–10 –8
–6
–4
–2
–2
–4
–4
–6
–6
–8
–8
–10
–10
18. Write a function that transforms
2
4
6
8
10
x
in the following way:
stretch vertically by a factor of 6 and shift 5 units left.
a.
c.
b.
d.
19. Using the graph of
as a guide, describe the transformations, and then graph the function
.
a.
is
translated 2 units right and 6 units up.
y
10
8
g(x)
6
4
f(x)
2
–10 –8
–6
–4
–2
–2
2
4
6
8
10
x
–4
–6
–8
–10
b.
is
translated 6 units left and 2 units down.
y
10
8
6
4
f(x)
2
–10 –8
–6
–4
g(x)
–2
–2
2
4
6
8
10
x
–4
–6
–8
–10
c.
is
translated 2 units left and 6 units down.
y
10
8
g(x)
6
4
2
–10 –8
–6
–4
–2
–2
f(x)
2
4
6
8
10
x
–4
–6
–8
–10
d.
is
translated 6 units right and 2 units up.
y
10
8
6
4
2
–10 –8
–6
–4
g(x)
–2
–2
f(x)
2
4
6
8
10
x
–4
–6
–8
–10
20. The parent function
is reflected across the x-axis, vertically stretched by a factor of 10, and
translated right 10 units to create g. Use the description to write the quadratic function in vertex form.
a.
c.
b.
d.
21. The minimum braking distance d in feet for a properly loaded truck on dry concrete is approximated by
the function
, where v is the vehicle’s speed in miles per hour. If the truck is overloaded,
the braking-distance function is
. What kind of transformation describes this change, and
what does the transformation mean?
a. The value of a has increased from 0.065 to 0.078. The increase indicates a vertical stretch
by a factor of 1.2. Thus, an overloaded truck takes about 1.2 times as many feet to stop as
a properly loaded truck.
b. The value of a has increased from 0.065 to 0.078. The increase indicates a vertical stretch
by a factor of 1.2. Thus, a properly loaded truck takes about 1.2 times as many feet to stop
as an overloaded truck.
c. The value of a has increased from 0.065 to 0.078. The increase indicates a horizontal
stretch by a factor of 1.2. Thus, an overloaded truck takes about 1.2 times as many feet to
stop as properly loaded truck.
d. The value of a has increased from 0.065 to 0.078. The increase indicates a horizontal
stretch by a factor of 1.2. Thus, a properly loaded truck takes about 1.2 times as many feet
to stop as an overloaded truck.
22. Identify the axis of symmetry for the graph of
a.
c.
b.
d.
.
23. Find the minimum or maximum value of
. Then state the domain and range of the
function.
a. The maximum value is 1. D: {all real numbers}; R: {y | y  –7}
b. The minimum value is –7. D: {x | x  –7 }; R: {all real numbers}
c. The maximum value is 1. D: {x | x  –7 }; R: {all real numbers}
d. The minimum value is –7. D: {all real numbers}; R: {y | y  –7}
24. Find the zeros of the function
by factoring.
a.
b.
c.
d.
or
or
25. Find the roots of the equation
a.
b.
or
or
by factoring.
c.
d.
26. Write a quadratic function in standard form with zeros 6 and –8.
a.
c.
b.
d.
27. Solve the equation
a.
3 6
b.
3 6
.
c.
d.
3 6
28. Complete the square for the expression
squared.
a.
b.
____. Write the resulting expression as a binomial
c.
d.
29. Express
a. 16i
b.
c. 16 21
d. 16i 21
in terms of i.
21
30. Solve the equation
a.
b.
.
c.
d.
31. Find the zeros of the function
a. x = 3 or –3
b. x = –3 + 3 or –3 – 3
.
c. x = –3 + 3
d. x = –6 + 3 or –6 – 3
32. Find the number and type of solutions for
.
a. Cannot determine without graphing.
b. The equation has one real solution.
c. The equation has two nonreal complex solutions.
d. The equation has two real solutions.
33. During the eruption of Mount St. Helens in 1980, debris was ejected at a speed of over 440 feet per
second (300 miles per hour). The height in feet of a rock ejected at angle of 75° is given by the equation
, where t is the time in seconds after the eruption. The rock’s horizontal
distance in feet from the point of ejection is given by
. Assuming the elevation of the
surrounding countryside is 0 feet, what is the horizontal distance from the point of ejection to the where
the rock would have landed? Round your answer to the nearest foot.
a. 2,234 ft
c. 4,467 ft.
b. 8,932 ft
d. 1,117 ft
34. Subtract. Write the result in the form
.
(5 – 2 ) – (6 + 8 )
a. –1 – 10
b. 7 – 2
35. Multiply
a.
b.
36. Simplify
a.
b.
c.
d.
37. Multiply
c. –3 – 8
d. 11 + 6
. Write the result in the form
. Identify any x-values for which the expression is undefined.
; The expression is undefined at
.
; The expression is undefined at
.
; The expression is undefined at
and
; The expression is undefined at
and
.
c.
d.
. Assume that all expressions are defined.
a.
c.
b.
d.
39. Solve
.
. Assume that all expressions are defined.
a.
b.
38. Divide
.
c.
d.
. Check your answer.
a.
b. There is no solution because the original equation is undefined at
c.
d.
40. Subtract
.
. Identify any x-values for which the expression is undefined.
a.
; The expression is undefined at x = ±3.
b.
; The expression is always defined.
c.
; The expression is always defined.
d.
; The expression is undefined at x = ±3.
41. Add
a.
. Identify any x-values for which the expression is undefined.
c.
;
;
The expression is undefined at
b.
.
The expression is undefined at
.
d.
;
The expression is undefined at
.
42. Simplify
and
;
The expression is undefined at
.
. Assume that all expressions are defined.
a.
c.
b.
d.
43. Identify the asymptotes, domain, and range of the function
a. Vertical asymptote:
Domain:
Horizontal asymptote:
Range:
b. Vertical asymptote:
Domain:
Horizontal asymptote:
Range:
44. Identify the zeros and vertical asymptotes of
a. Zeros at and .
Vertical asymptote:
and
.
c. Vertical asymptote:
Domain:
Horizontal asymptote:
Range:
d. Vertical asymptote:
Domain:
Horizontal asymptote:
Range:
. Then graph.
c. Zeros at and .
Vertical asymptote:
and
y
–20
y
20
20
10
10
–10
10
x
20
–20
–10
–10
–10
–20
–20
b. Zeros at
and .
Vertical asymptote:
20
20
10
10
–10
10
x
20
–20
–10
–10
–10
–20
–20
x
.
y
10
10
8
8
6
6
4
4
2
2
–2
–2
20
c. There is a hole in the graph at
.
y
–4
10
. Then graph.
a. There is a hole in the graph at
–6
x
y
45. Identify holes in the graph of
–10 –8
20
d. Zeros at
and .
Vertical asymptote:
y
–20
10
2
4
6
8
10
x
–10 –8
–6
–4
–2
–2
–4
–4
–6
–6
–8
–8
–10
–10
2
4
6
8
10
x
b. There are no holes in the graph.
d. There is a hole in the graph at
y
–10 –8
–6
–4
10
10
8
8
6
6
4
4
2
2
–2
–2
a.
b.
4
6
8
10
x
–6
–4
–2
–2
–6
–6
–8
–8
–10
–10
2
4
6
8
10
x
.
c.
d.
or
or
.
c.
3
2
b.
d. There is no solution.
48. Simplify the expression
a.
b.
49. Write the expression
a.
;3
b.
–10 –8
–4
47. Solve the equation
a.
2
–4
46. Solve the equation
.
y
; 32
50. Simplify the expression
a. 729
b. 3
. Assume that all variables are positive.
c.
d.
in radical form, and simplify. Round to the nearest whole number if necessary.
c.
; 32
d.
; 64
.
51. The surface area S of a cube with volume V is
by a factor of 7 have on the on the surface area?
a. The surface area increases by a factor of 7.
b. The surface area increases by a factor of .
c. 9
d. 27
. What effect does increasing the volume of a cube
c.
The surface area increases by a factor of
.
d.
The surface area increases by a factor of
.
52. Using the graph of
as a guide, describe the transformation and graph
a. Stretch f vertically by a factor of 4 and
c. Compress f horizontally by a factor of
translate it right 3 units.
and translate it down 3 units.
y
.
y
10
10
8
8
6
6
4
4
2
2
–10 –8
–6
–4
–2
–2
2
4
6
8
10
x
–10 –8
–6
–4
–4
–2
–2
2
4
6
8
10
x
–4
–6
–6
–8
–8
–10
–10
b. Stretch f vertically by a factor of 4 and
translate it left 3 units.
d. Compress f horizontally by a factor of
and translate it up 3 units.
y
y
10
10
8
8
6
6
4
4
2
2
–10 –8
–6
–4
–2
–2
2
4
6
8
10
x
–10 –8
–4
–6
–4
–2
–2
2
4
6
8
10
x
–4
–6
–6
–8
–8
–10
–10
53. The function g is a translation 3 units left and 2 units up of
a.
c.
b.
54. Solve the equation
a.
b.
d.
.
c.
d.
. Write the function g(x).
55. Solve
a. x = 14
b. x = 11
.
c. x = 9
d. x = 18
56. Solve
a. No solution.
.
c. x = 5
is not defined for
b.
.
d. x = –6
or
57. Mira bought $300 of Freerange Wireless stock in January of 1998. The value of the stock is expected to
increase by 7.5% per year. Use a graph to predict the year the value of Mira’s stock will reach $700.
a. 2004
c. 2014
b. 1999
d. 2009
58. A bacteria population starts at 2,032 and decreases at about 15% per day. Write a function representing
the number of bacteria present each day. Graph the function. After how many days will there be fewer
than 321 bacteria?
a.
c.
y
y
1500
1500
1200
1200
900
900
600
600
300
300
1
2
x
3
After about 1.05 days, there will be fewer
than 321 bacteria.
b.
6
9
12
x
After about 11.3 days, there will be fewer
than 321 bacteria.
d.
y
y
1500
1500
1200
1200
900
900
600
600
300
300
3
6
9
12
x
After about 0.19 days, there will be fewer
1
2
x
After about 0.97days, there will be fewer
than 321 bacteria.
than 321 bacteria.
59. A initial investment of $10,000 grows at
investment after t years?
a.
b.
per year. What function represents the value of the
c.
d.
2
3
60. Use inverse operations to write the inverse of
.
a.
2
3
c.
1
3
b.
1
3
d.
2
3
61. Write the exponential equation
a.
b.
62. Write the logarithmic equation
a.
b.
63. Simplify
a.
b.
in logarithmic form.
c.
d.
in exponential from.
c.
d.
.
c.
d.
64. The amount of money in a bank account can be expressed by the exponential equation
where A is the amount in dollars and t is the time in years. About how many years will it take for the
amount in the account to be more than $900?
a. 19 years
c. 221 years
b. 30 years
d. 37 years
65. Solve
a.
.
c.
b.
66. Simplify
a. –5
b.
67.
d.
.
c.
d. –5x
is transformed 4 units left, compressed vertically by a factor of , and reflected across the x-
axis. Write the transformed function
a.
b.
.
c.
d.
68. What function is vertically stretched by a factor of 3 and translated 4 units right from the parent function?
a.
c.
b.
d.