Name: ______________________ Class: _________________ Date: _________
ID: A
Algebra 2 Chapter 5 Practice Test (Review)
Multiple Choice
Identify the choice that best completes the statement or answers the question.
Determine whether the function is linear or quadratic. Identify the quadratic, linear, and
constant terms.
____
____
1. y = (x + 1)(6x − 6) − 6x 2
a. linear function
c. linear function
linear term: −35x
linear term: 0x
constant term: 6
constant term: –6
b. quadratic function
d. quadratic function
quadratic term: 6x 2
quadratic term: −6x 2
linear term: −35x
linear term: 0x
constant term: 6
constant term: –6
2. Find a quadratic function to model the values in the table. Predict the value of y for x = 6.
x
y
–1
2
0
–2
3
10
a.
____
y = −2x 2 + 2x − 2; –58
c. y = 2x 2 − 2x − 2; 58
b. y = 2x 2 − 2x − 2; 60
d. y = −2x 2 + 2x + 2; –58
3. A biologist took a count of the number of migrating waterfowl at a particular lake, and recounted the
lake’s population of waterfowl on each of the next six weeks.
Week
0
1
2
3
4
5
6
Population
a.
585
582
629
726
873
1,070 1,317
b.
Find a quadratic function that models the data as a function of x, the number of
weeks.
Use the model to estimate the number of waterfowl at the lake on week 8.
a.
b.
c.
d.
P(x)
P(x)
P(x)
P(x)
=
=
=
=
25x 2
30x 2
25x 2
30x 2
−
+
−
+
28x
28x
28x
28x
+
+
+
+
585; 1,614 waterfowl
535; 2,679 waterfowl
585; 1,961 waterfowl
535; 2,201 waterfowl
1
Name: ______________________
____
____
4. Dalco Manufacturing estimates that its weekly profit, P, in hundreds of dollars, can be approximated
by the formula P = −3x 2 + 6x + 10, where x is the number of units produced per week, in
thousands.
a. How many units should the company produce per week to earn the maximum
profit?
b. Find the maximum weekly profit.
a. 1,000 units; $1300
c. 1,000 units; $600
b. 3,000 units; $100
d. 2,000 units; $1100
5. Use vertex form to write the equation of the parabola.
a.
____
ID: A
y = 3(x − 2) 2 + 2
c. y = 3(x + 2) 2 + 2
b. y = 3(x − 2) 2 − 2
d. y = (x + 2) 2 + 2
6. Use vertex form to write the equation of the parabola.
a.
y = (x − 2) 2 − 2
c. y = −(x − 2) 2 − 2
b.
y = −(x + 2) 2 + 2
d. y = −(x + 2) 2 − 2
2
Name: ______________________
____
ID: A
7. Write y = 2x 2 + 12x + 14 in vertex form.
a.
y = 2(x + 12) 2 + 14
c. y = (x + 3) 2 + 14
b.
y = 6(x + 9) 2 − 4
d. y = 2(x + 3) 2 − 4
Write the equation of the parabola in vertex form.
____
____
8. vertex (4, –2), point (0, –50)
a. y = (x + 4) 2 − 2
b. y = −3(x − 4) 2 − 2
9. vertex (–3, –2), point (–2, –6)
a. y = −4(x + 3) 2 − 2
b. y = − 2(x − 3) 2 − 2
c. y = − 50(x − 4) 2 + 2
d. y = −3(x + 4) 2 − 2
c. y = −4(x − 3) 2 − 2
d. y = − 6(x + 3) 2 + 2
Factor the expression.
____
____
____
____
____
____
____
____
10. −15x 2 − 21x
a. x(−15x − 21)
b. −15x(x + 7)
c. −3x(5x + 7)
d. 5x(x − 3 + 7)
11. 8x 2 + 12x − 16
a. −2(−4x 2 + 12x − 16)
b. 8x 2 + 12x − 16
c. 8x(−2x − 3)
d. −4(−2x 2 − 3x + 4)
12. x 2 + 14x + 48
a. (x + 6)(x − 8)
b. (x + 8)(x − 6)
c. (x − 8)(x − 6)
d. (x + 6)(x + 8)
13. x 2 − 6x + 8
a. (x + 4)(x + 2)
b. (x − 2)(x − 4)
c. (x − 4)(x + 2)
d. (x − 2)(x + 4)
14. x 2 − 2x − 63
a. (x − 9)(x + 7)
b. (x + 7)(x + 9)
c. (x − 9)(x − 7)
d. (x − 7)(x + 9)
15. 3x 2 + 26x + 35
a. (x + 5)(3x + 7)
b. (3x + 7)(x − 5)
c. (3x + 5)(x − 7)
d. (3x + 5)(x + 7)
16. 5x 2 − 22x − 15
a. (5x + 3)(x + 5)
b. (x + 3)(5x − 5)
c. (5x + 3)(x − 5)
d. (5x − 5)(x − 3)
17. 16x 2 + 40x + 25
a. (4x − 5) 2
b. (4x + 5)(−4x − 5)
c. (4x + 5) 2
d. (−4x + 5) 2
3
Name: ______________________
____
____
ID: A
18. 9x 2 − 16
a. (3x + 4)(−3x − 4)
b. (3x + 4)(3x − 4)
19. Solve by factoring.
4x 2 + 28x − 32 = 0
a. 8, − 1
b. –8, 4
2
c. (−3x + 4)(3x − 4)
d. (3x − 4) 2
d. 1, − 1
2
c. –8, 1
Solve the equation by finding square roots.
____
____
20. 3x 2 = 21
a.
7
b.
7,–
c.
21
3
d. − 7 ,
7
21. 108x 2 = 147
a. − 49 , 49
36 36
−
b. − 7 , 7
6 6
21
,
3
21
c. − 6 , 6
7 7
d. − 36 , 36
49 49
____
22. The function y = −16t 2 + 486 models the height y in feet of a stone t seconds after it is dropped
from the edge of a vertical cliff. How long will it take the stone to hit the ground? Round to the
nearest hundredth of a second.
a. 7.79 seconds
c. 0.25 seconds
b. 11.02 seconds
d. 5.51 seconds
____
23. Use a graphing calculator to solve the equation 5x 2 + 6x − 9 = 0. If necessary, round to the nearest
hundredth.
a. 1.47, –1.47
c. 0.87, –2.07
b. 1.74, –4.14
d. 2.07, –0.87
____
24. Simplify −175 using the imaginary number i.
a. i 175
b. 5i 7
c. 5
−7
Write the number in the form a + bi.
____
25.
a.
b.
____
____
−4 + 10
4 + 10i
10 + i 4
c. 10 + 2i
d. 2 + 10i
26. –6 – −48
a. 6 + i 48
b. −6 − 4i 3
27. Find the additive inverse of −7 + 5i.
a. −7 − 5i
b. −7 + 5i
c. 6 − 4i 3
d. −6 + 4i 3
c. 7 − 5i
d. 7 + 5i
4
d. −5
7
Name: ______________________
ID: A
Simplify the expression.
____
____
____
____
28. (−1 + 6i) + (−4 + 2i)
a. 5 − 8i
b. 5 − 2i
29. (2 − 5i) − (3 + 4i)
a. 1 + 9i
b. 5 − i
30. (−6i)(−6i)
a. 36
b. –36
31. (2 + 5i)(−1 + 5i)
a. −27 + 5i
b. 23 + 5i
c. −5 + 8i
d. 3i
c. −1 − 9i
d. −10i
c. –36i
d. 36i
c. −2 + 25i
d. −2 + 5i
Solve the equation.
____
____
32. 9x 2 + 16 = 0
a. − 4 i, 4 i
3 3
b. − 16 i, 16 i
9
9
c. − 3 i, 3 i
4 4
d. − 4 , 4
3 3
33. x 2 + 18x + 81 = 25
a. 14, 4
b. –4, –14
c. 14, –14
d. –4, 4
Solve the quadratic equation by completing the square.
____
____
____
____
34. x 2 + 10x + 14 = 0
a. −10 ± 6
b. 100 ± 11
c. 5 ± 6
d. −5 ±
11
2
35. x + 10x + 35 = 0
a. −10 ± 15
b. 5 ± i 15
c. 100 ± i 10
d. −5 ± i 10
36. x 2 + 16x + 66 = 0
a. 256 ± i 2
b. 8 ± i 62
c. −8 ± i 2
d. −16 ± 62
37. x 2 + 12x + 41 = 0
a. 6 ± i 31
b. −6 ± i 5
c. 144 ± i 5
d. −12 ± 31
5
Name: ______________________
ID: A
Use the Quadratic Formula to solve the equation.
____
____
____
____
38. 5x 2 + 9x − 2 = 0
a. 2 , −4
5
1 , −2
5
b.
56 , −13
5
c.
1 ±
2
d.
1 ±
4
39. −2x 2 + x + 8 = 0
65
a. 1 ±
4
4
130
b. 4 ±
4
c.
40. 4x 2 − x + 3 = 0
47
a. 1 ±
8
8
i 94
b. 8 ±
8
c.
d.
41. 8x 2 − 5x − 10 = 0
a. 1.16, –1.16
b. 1.47, –0.85
d. 2, − 1
5
65
2
32
2
1 ± i 47
8
8
1 ± i 47
4
4
c. 2.95, –1.7
d. 0.85, –1.47
Short Answer
42. In an experiment, a petri dish with a colony of bacteria is exposed to cold temperatures and then
warmed again.
a. Find a quadratic model for the data in the table.
b. Use the model to estimate the population of bacteria at 9 hours.
Time (hours)
Population (1000s)
0
5.1
1
2
3
4
3.03 1.72 1.17 1.38
6
5
6
2.35
4.08
Name: ______________________
ID: A
43. Graph y = x 2 + 3x + 2. Identify the vertex and the axis of symmetry.
44. Graph y = 3x 2 − 12x + 13. What is the minimum value of the function?
45. Graph y = −3x 2 + 6x + 5. Does the function have a maximum or minimum value? What is this
value?
7
Name: ______________________
ID: A
46. A science museum is going to put an outdoor restaurant along one wall of the museum. The
restaurant space will be rectangular. Assume the museum would prefer to maximize the area for the
restaurant.
a. Suppose there is 120 feet of fencing available for the three sides that require
fencing. How long will the longest side of the restaurant be?
b. What is the maximum area?
47. Graph y = (x − 7) 2 + 5.
48. Suppose you cut a small square from a square of fabric as shown in the diagram. Write an
expression for the remaining shaded area. Factor the expression.
49. The Sears Tower in Chicago is 1454 feet tall. The function y = −16t 2 + 1454 models the height y in
feet of an object t seconds after it is dropped from the top of the building.
a. After how many seconds will the object hit the ground? Round your answer to the
nearest tenth of a second.
b. What is the height of the object 5 seconds after it is dropped from the top of the
Sears Tower?
8
ID: A
Algebra 2 Chapter 5 Practice Test (Review)
Answer Section
MULTIPLE CHOICE
1. ANS:
REF:
OBJ:
STA:
KEY:
2. ANS:
REF:
OBJ:
TOP:
3. ANS:
REF:
OBJ:
TOP:
KEY:
4. ANS:
REF:
STA:
KEY:
5. ANS:
REF:
STA:
KEY:
6. ANS:
REF:
STA:
KEY:
7. ANS:
REF:
STA:
KEY:
8. ANS:
REF:
STA:
KEY:
9. ANS:
REF:
STA:
KEY:
C
PTS: 1
DIF: L2
5-1 Modeling Data With Quadratic Functions
5-1.1 Quadratic Functions and Their Graphs
CO 2.1 | CO 2.2 | CO 2.6 | CO 2.4 TOP: 5-1 Example 1
quadratic function | quadratic term | linear term | constant term
C
PTS: 1
DIF: L3
5-1 Modeling Data With Quadratic Functions
5-1.2 Using Quadratic Models
STA: CO 2.1 | CO 2.2 | CO 2.6 | CO 2.4
5-1 Example 3
KEY: quadratic function | quadratic model
C
PTS: 1
DIF: L2
5-1 Modeling Data With Quadratic Functions
5-1.2 Using Quadratic Models
STA: CO 2.1 | CO 2.2 | CO 2.6 | CO 2.4
5-1 Example 4
quadratic model | quadratic function | word problem | problem solving | multi-part question
A
PTS: 1
DIF: L3
5-2 Properties of Parabolas
OBJ: 5-2.2 Finding Maximum and Minimum Values
CO 2.4 | CO 2.5
TOP: 5-2 Example 4
maximum value | word problem | problem solving | multi-part question
C
PTS: 1
DIF: L2
5-3 Translating Parabolas
OBJ: 5-3.1 Using Vertex Form
CO 2.4 | CO 2.5 | CO 4.1
TOP: 5-3 Example 2
parabola | equation of a parabola | vertex form
C
PTS: 1
DIF: L2
5-3 Translating Parabolas
OBJ: 5-3.1 Using Vertex Form
CO 2.4 | CO 2.5 | CO 4.1
TOP: 5-3 Example 2
parabola | equation of a parabola | vertex form
D
PTS: 1
DIF: L2
5-3 Translating Parabolas
OBJ: 5-3.1 Using Vertex Form
CO 2.4 | CO 2.5 | CO 4.1
TOP: 5-3 Example 4
parabola | vertex form
B
PTS: 1
DIF: L3
5-3 Translating Parabolas
OBJ: 5-3.1 Using Vertex Form
CO 2.4 | CO 2.5 | CO 4.1
TOP: 5-3 Example 2
parabola | equation of a parabola | vertex form
A
PTS: 1
DIF: L3
5-3 Translating Parabolas
OBJ: 5-3.1 Using Vertex Form
CO 2.4 | CO 2.5 | CO 4.1
TOP: 5-3 Example 2
parabola | equation of a parabola | vertex form
1
ID: A
10. ANS: C
PTS: 1
DIF: L2
REF: 5-4 Factoring Quadratic Expressions
OBJ: 5-4.1 Finding Common and Binomial Factors
TOP: 5-4 Example 1
KEY: factor a quadratic expression | quadratic expression | greatest common factor of an
expression
11. ANS: D
PTS: 1
DIF: L2
REF: 5-4 Factoring Quadratic Expressions
OBJ: 5-4.1 Finding Common and Binomial Factors
TOP: 5-4 Example 1
KEY: factor a quadratic expression | quadratic expression | greatest common factor of an
expression
12. ANS: D
PTS: 1
DIF: L2
REF: 5-4 Factoring Quadratic Expressions
OBJ: 5-4.1 Finding Common and Binomial Factors
TOP: 5-4 Example 2
KEY: factor a quadratic expression | quadratic expression
13. ANS: B
PTS: 1
DIF: L2
REF: 5-4 Factoring Quadratic Expressions
OBJ: 5-4.1 Finding Common and Binomial Factors
TOP: 5-4 Example 3
KEY: factor a quadratic expression | quadratic expression
14. ANS: A
PTS: 1
DIF: L2
REF: 5-4 Factoring Quadratic Expressions
OBJ: 5-4.1 Finding Common and Binomial Factors
TOP: 5-4 Example 4
KEY: factor a quadratic expression | quadratic expression
15. ANS: D
PTS: 1
DIF: L2
REF: 5-4 Factoring Quadratic Expressions
OBJ: 5-4.1 Finding Common and Binomial Factors
TOP: 5-4 Example 5
KEY: factor a quadratic expression | quadratic expression
16. ANS: C
PTS: 1
DIF: L2
REF: 5-4 Factoring Quadratic Expressions
OBJ: 5-4.1 Finding Common and Binomial Factors
TOP: 5-4 Example 6
KEY: factor a quadratic expression | quadratic expression
17. ANS: C
PTS: 1
DIF: L2
REF: 5-4 Factoring Quadratic Expressions
OBJ: 5-4.2 Factoring Special Expressions
TOP: 5-4 Example 7
KEY: factor a quadratic expression | factor a trinomial | perfect square trinomial
18. ANS: B
PTS: 1
DIF: L2
REF: 5-4 Factoring Quadratic Expressions
OBJ: 5-4.2 Factoring Special Expressions
TOP: 5-4 Example 8
KEY: difference of two squares | factoring a difference of two squares
19. ANS: C
PTS: 1
DIF: L2
REF: 5-5 Quadratic Equations
OBJ: 5-5.1 Solving by Factoring and Finding Square Roots
STA: CO 2.4 | CO 2.5
TOP: 5-5 Example 1
KEY: factor a quadratic expression
20. ANS: B
PTS: 1
DIF: L2
REF: 5-5 Quadratic Equations
OBJ: 5-5.1 Solving by Factoring and Finding Square Roots
STA: CO 2.4 | CO 2.5
TOP: 5-5 Example 2
KEY: square root
21. ANS: B
PTS: 1
DIF: L2
REF: 5-5 Quadratic Equations
OBJ: 5-5.1 Solving by Factoring and Finding Square Roots
STA: CO 2.4 | CO 2.5
TOP: 5-5 Example 2
KEY: square root
2
ID: A
22. ANS:
OBJ:
TOP:
KEY:
23. ANS:
OBJ:
TOP:
24. ANS:
OBJ:
KEY:
25. ANS:
OBJ:
KEY:
26. ANS:
OBJ:
KEY:
27. ANS:
OBJ:
KEY:
28. ANS:
OBJ:
KEY:
29. ANS:
OBJ:
KEY:
30. ANS:
OBJ:
KEY:
31. ANS:
OBJ:
KEY:
32. ANS:
OBJ:
KEY:
33. ANS:
REF:
OBJ:
STA:
KEY:
34. ANS:
REF:
OBJ:
STA:
KEY:
D
PTS: 1
DIF: L2
REF: 5-5 Quadratic Equations
5-5.1 Solving by Factoring and Finding Square Roots
STA: CO 2.4 | CO 2.5
5-5 Example 3
round a number | word problem | problem solving
C
PTS: 1
DIF: L2
REF: 5-5 Quadratic Equations
5-5.2 Solving by Graphing
STA: CO 2.4 | CO 2.5
5-5 Example 5
KEY: graphing calculator | round a number
B
PTS: 1
DIF: L2
REF: 5-6 Complex Numbers
5-6.1 Identifying Complex Numbers
TOP: 5-6 Example 1
i | imaginary number
C
PTS: 1
DIF: L2
REF: 5-6 Complex Numbers
5-6.1 Identifying Complex Numbers
TOP: 5-6 Example 2
i | imaginary number | complex number
B
PTS: 1
DIF: L2
REF: 5-6 Complex Numbers
5-6.1 Identifying Complex Numbers
TOP: 5-6 Example 2
i | imaginary number | complex number
C
PTS: 1
DIF: L2
REF: 5-6 Complex Numbers
5-6.2 Operations With Complex Numbers
TOP: 5-6 Example 4
additive inverse | complex number
C
PTS: 1
DIF: L2
REF: 5-6 Complex Numbers
5-6.2 Operations With Complex Numbers
TOP: 5-6 Example 5
simplifying a complex number | complex number
C
PTS: 1
DIF: L2
REF: 5-6 Complex Numbers
5-6.2 Operations With Complex Numbers
TOP: 5-6 Example 5
simplifying a complex number | complex number
B
PTS: 1
DIF: L2
REF: 5-6 Complex Numbers
5-6.2 Operations With Complex Numbers
TOP: 5-6 Example 6
simplifying a complex number | complex number | multiplying complex numbers
A
PTS: 1
DIF: L2
REF: 5-6 Complex Numbers
5-6.2 Operations With Complex Numbers
TOP: 5-6 Example 6
simplifying a complex number | complex number | multiplying complex numbers
A
PTS: 1
DIF: L2
REF: 5-6 Complex Numbers
5-6.2 Operations With Complex Numbers
TOP: 5-6 Example 7
complex number | imaginary number
B
PTS: 1
DIF: L2
5-7 Completing the Square
5-7.1 Solving Equations by Completing the Square
CO 2.1 | CO 2.2 | CO 2.3 | CO 2.4 TOP: 5-7 Example 1
perfect square trinomial
D
PTS: 1
DIF: L2
5-7 Completing the Square
5-7.1 Solving Equations by Completing the Square
CO 2.1 | CO 2.2 | CO 2.3 | CO 2.4 TOP: 5-7 Example 3
completing the square
3
ID: A
35. ANS:
REF:
OBJ:
STA:
KEY:
36. ANS:
REF:
OBJ:
STA:
KEY:
37. ANS:
REF:
OBJ:
STA:
KEY:
38. ANS:
REF:
TOP:
39. ANS:
REF:
TOP:
40. ANS:
REF:
TOP:
41. ANS:
OBJ:
TOP:
D
PTS: 1
DIF: L2
5-7 Completing the Square
5-7.1 Solving Equations by Completing the Square
CO 2.1 | CO 2.2 | CO 2.3 | CO 2.4 TOP: 5-7 Example 4
completing the square
C
PTS: 1
DIF: L2
5-7 Completing the Square
5-7.1 Solving Equations by Completing the Square
CO 2.1 | CO 2.2 | CO 2.3 | CO 2.4 TOP: 5-7 Example 4
completing the square
B
PTS: 1
DIF: L2
5-7 Completing the Square
5-7.1 Solving Equations by Completing the Square
CO 2.1 | CO 2.2 | CO 2.3 | CO 2.4 TOP: 5-7 Example 4
completing the square
B
PTS: 1
DIF: L2
5-8 The Quadratic Formula
OBJ: 5-8.1 Using the Quadratic Formula
5-8 Example 1
KEY: Quadratic Formula
A
PTS: 1
DIF: L2
5-8 The Quadratic Formula
OBJ: 5-8.1 Using the Quadratic Formula
5-8 Example 1
KEY: Quadratic Formula
C
PTS: 1
DIF: L2
5-8 The Quadratic Formula
OBJ: 5-8.1 Using the Quadratic Formula
5-8 Example 2
KEY: Quadratic Formula
B
PTS: 1
DIF: L2
REF: 5-5 Quadratic Equations
5-5.2 Solving by Graphing
STA: CO 2.4 | CO 2.5
5-5 Example 4
KEY: graphing calculator | round a number
SHORT ANSWER
42. ANS:
a. P = 0.38x 2 − 2.45x + 5.10
b. 13,830 bacteria
PTS:
OBJ:
TOP:
KEY:
1
DIF: L2
REF: 5-1 Modeling Data With Quadratic Functions
5-1.2 Using Quadratic Models
STA: CO 2.1 | CO 2.2 | CO 2.6 | CO 2.4
5-1 Example 4
quadratic model | quadratic function | problem solving | word problem | multi-part question
4
ID: A
43. ANS:
ÁÊÁ 3
1 ˜ˆ˜
3
vertex: ÁÁÁÁ − , − ˜˜˜˜ , axis of symmetry: x = −
ÁË 2
4 ˜¯
2
PTS:
OBJ:
TOP:
KEY:
44. ANS:
1
DIF: L2
REF: 5-2 Properties of Parabolas
5-2.1 Graphing Parabolas
STA: CO 2.4 | CO 2.5
5-2 Example 2
quadratic function | vertex of a parabola | axis of symmetry
minimum: 1
PTS: 1
DIF: L2
REF: 5-2 Properties of Parabolas
OBJ: 5-2.2 Finding Maximum and Minimum Values
STA: CO 2.4 | CO 2.5
TOP: 5-2 Example 3
KEY: quadratic function | minimum value
5
ID: A
45. ANS:
maximum value; 8
PTS: 1
DIF: L2
REF: 5-2 Properties of Parabolas
OBJ: 5-2.2 Finding Maximum and Minimum Values
STA: CO 2.4 | CO 2.5
TOP: 5-2 Example 3
KEY: quadratic function | minimum value | maximum value
46. ANS:
a. 40 ft
b. 1,600 ft 2
PTS: 1
DIF: L3
REF: 5-2 Properties of Parabolas
OBJ: 5-2.2 Finding Maximum and Minimum Values
STA: CO 2.4 | CO 2.5
TOP: 5-2 Example 3
KEY: maximum value | quadratic function | area | problem solving | word problem | multi-part
question
6
ID: A
47. ANS:
PTS: 1
DIF: L2
OBJ: 5-3.1 Using Vertex Form
TOP: 5-3 Example 1
48. ANS:
x 2 − 9; (x − 3)(x + 3)
REF: 5-3 Translating Parabolas
STA: CO 2.4 | CO 2.5 | CO 4.1
KEY: graphing | translation | parabola
PTS: 1
DIF: L2
REF: 5-4 Factoring Quadratic Expressions
OBJ: 5-4.2 Factoring Special Expressions
TOP: 5-4 Example 8
KEY: difference of two squares | factoring a difference of two squares
49. ANS:
a. 9.5 seconds
b. 1,054 ft
PTS:
OBJ:
TOP:
KEY:
1
DIF: L3
REF: 5-5 Quadratic Equations
5-5.1 Solving by Factoring and Finding Square Roots
STA: CO 2.4 | CO 2.5
5-5 Example 3
round a number | word problem | problem solving | multi-part question
7