Name: ________________________ Class: ___________________ Date: __________ ID: A
1
Algebra 2 Chapter 4
What is the graph of the function?
1. f(x) = 2x2
2. f(x) =1
3x
2
Graph each function. How is each graph a translation of f(x) = x2?
3. y = (x + 3)2
+ 4
____ 4. Identify the vertex and the axis of symmetry of the graph of the function y = 2(x + 2)2
− 4.
a. vertex: (–2, 4);
axis of symmetry: x = −2
b. vertex: (2, –4);
axis of symmetry: x = 2
c. vertex: (–2, –4);
axis of symmetry: x = −2
d. vertex: (2, 4);
axis of symmetry: x = 2
____ 5. Identify the maximum or minimum value and the domain and range of the graph of the function
y = 2(x + 2)2
− 3.
a. minimum value: 3
domain: all real numbers ≥ 3
range: all real numbers
b. maximum value: –3
domain: all real numbers ≤ −3
range: all real numbers
c. maximum value: 3
domain: all real numbers
range: all real numbers ≤ 3
d. minimum value: –3
domain: all real numbers
range: all real numbers ≥ −3
Name: ________________________ ID: A
2
____ 6. Which is the graph of y = −2(x − 2)2
− 4?
a. c.
b. d.
7. Use the vertex form to write the equation of the parabola. Then rewrite in standard form.
8. Suppose a parabola has vertex (–8, –7) and also passes through the point (–7, –4). Write the equation of the
parabola in vertex form.
Name: ________________________ ID: A
3
____ 9. Suppose a parabola has an axis of symmetry at x = −6, a maximum height of 6 and also passes through the
point (–5, 4). Write the equation of the parabola in vertex form.
a. y = −2(x − 6)2
+ 6 c. y = −2(x + 6)2
+ 6
b. y = (x + 6)2
+ 6 d. y = 2(x + 6)2
− 6
What are the vertex and the axis of symmetry of the equation?
____ 10. y = −2x2
+ 24x − 4
a. vertex: ( 6, 68)
axis of symmetry: x = 68
c. vertex: ( 6, 68)
axis of symmetry: x = 6
b. vertex: ( –6, 68)
axis of symmetry: x = −6
d. vertex: ( –6, –68)
axis of symmetry: y = −6
What is the maximum or minimum value of the function? What is the range?
____ 11. y = 2x2
+ 28x − 8
a. minimum value: 7
range: y ≥ 7
c. minimum value: –106
range: y ≥ −106
b. minimum value: –7
range: y ≥ −7
d. minimum value: –106
range: y ≥ −7
What is the graph of the equation?
12. y = x2
− 4x + 5
13. y = −x2
+ 2x + 3
14. y = −2x2
+ 2x + 2
What is the vertex form of the equation?
____ 15. y = x2
− 2x + 8
a. y = (x + 1)2
+ 7 c. y = (x − 1)2
+ 7
b. y = (x + 1)2
− 7 d. y = (x − 1)2
− 7
____ 16. y = x2
+ 8x − 6
a. y = (x − 4)2
− 22 c. y = (x + 4)2
− 22
b. y = (x − 4)2
+ 22 d. y = (x + 4)2
+ 22
Name: ________________________ ID: A
4
____ 17. y = −x2
+ 2x − 8
a. y = (x − 1)2
+ 7 c. y = −(x + 1)2
+ 7
b. y = −(x − 1)2
− 7 d. y = (x + 1)2
− 7
18. You live near a bridge that goes over a river. The underneath side of the bridge is an arch that can be
modeled with the function y = −0.000495x2
+ 0.619x where x and y are in feet. How high above the river is
the bridge (the top of the arch)? How long is the section of bridge above the arch?
What is the equation, in standard form, of a parabola that models the values in the table?
____ 19.
x –2 0 4
f(x) –8.5 4.5 –53.5
a. y = −4.5x2
− 0.5x + 3.5 c. y = −3.5x2
− 0.5x + 4.5
b. y = 3.5x2
+ 0.5x − 4.5 d. y = −0.5x2
− 3.5x + 4.5
____ 20. A historian took a count of the number of people in a Gold Rush town for six years in the 1870’s.
Year 1870 1871 1872 1873 1874 1875 1876
Population 370 386 392 388 374 350 316
Find a quadratic function that models the data as a function of x, the number of years since 1870. Use the
model to estimate the number of people in the town in 1888.
a. P(x) = −x2
− 21x + 320; 124 people
b. P(x) = −5x2
+ 21x + 370; 272 people
c. P(x) = −5x2
+ 21x + 370; 218 people
d. P(x) = −x2
− 21x + 320; 88 people
Name: ________________________ ID: A
5
____ 21. The table shows a meteorologist's predicted temperatures for an April day in Washington D.C starting at 8
A.M. Use a quadratic model of this data to predict the high temperature for the day. At what time does the
high temperature occur?
Time Predicted
Temperature (oF)
8 A.M. 48.91
10 A.M. 60.04
12 P.M. 67.11
2 P.M. 70.11
4 P.M. 69.05
6 P.M. 63.92
a. The predicted high temperature is 79.22 degrees Fahrenheit occurring at 2:29 P.M..
b. The predicted high temperature is 70.22 degrees Fahrenheit occurring at 2:29 P.M..
c. The predicted high temperature is 70.22 degrees Fahrenheit occurring at 3:29 P.M..
d. The predicted high temperature is 79.22 degrees Fahrenheit occurring at 3:29 P.M..
____ 22. You threw a rock off the balcony overlooking your backyard. The table shows the height of the rock at
different times. Use quadratic regression to find a quadratic model for this data.
Time
(in seconds)
Height
(in feet)
0 16
1 36.3
2 47.2
3 48.7
4 40.8
5 23.5
a. −5.2x2
+ 24x − 12 c. −4.2x2
+ 26x − 20
b. −4.7x2
+ 25x − 16 d. −4.7x2
− 25x + 16
What is the expression in factored form?
23. x2
− 15x + 50
24. −x2
+ 4x + 32
What is the expression in factored form?
25. −10x2
− 15x
26. 2x2
+ 16x + 30
Name: ________________________ ID: A
6
27. −4x2
+ 8x + 32
28. 3x2
+ 26x + 35
29. 16x2
− 40x + 25
30. 25x2
− 9
31. Suppose you cut a square into two rectangles as shown below. Write an expression for the area of the square.
What are the solutions of the quadratic equation?
32. x2
+ 11x = −28
33. 3x2
+ 25x + 42 = 0
34. The function y = −16t2
+ 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.
35. The function y = −0.024x2
+ 0.55x models the height y, in feet, of your pet frog's jump, where x is the
horizontal distance, in feet, from the start of the jump. How far did the frog jump? How high did it go?
Round your answer to the nearest hundredth.
36. The function h = −10t2
+ 95 models the path of a ball thrown by a boy where h represents height, in feet, and
t represents the time, in seconds, that the ball is in the air. Assuming the boy lives at sea level where h = 0 ft,
which is a likely place the boy could have been standing when he threw this ball?
What is the solution of each equation?
37. 3x2
= 21
38. 108x2
= 147
Name: ________________________ ID: A
7
____ 39. A landscaper is designing a flower garden in the shape of a trapezoid. She wants the length of the shorter
base to be 3 yards greater than the height, and the length of the longer base to be 5 yards greater than the
height. For what height will the garden have an area of 360 square yards? Round to the nearest tenth of a
yard. (Recall the formula for the area of a trapezoid = A =1
2h b 1 + b 2ÊËÁÁ ˆ
¯˜̃
a. 17.1 yards c. 39.2 yards
b. 34.2 yards d. 152.6 yards
____ 40. The lengths of the sides of a rectangular window have the ratio 1.2 to 1. The area of the window is 1920
square inches. What are the dimensions of the window?
a. 40 inches by 57.6 inches c. 40 inches by 80 inches
b. 40 inches by 48 inches d. 43.82 inches by 43.82 inches
Solve the equation.
____ 41. x2
+ 18x + 81 = 25
a. 14, 4 c. 14, –14
b. –4, –14 d. –4, 4
____ 42. x2
− 8x + 16 = 16
a. –8, 8 c. 0, 8
b. –8, 0 d. 0, 0
Solve the quadratic equation by completing the square.
____ 43. x2
+ 10x + 14 = 0
a. −10 ± 6 c. 5 ± 6
b. 100 ± 11 d. −5 ± 11
____ 44. −3x2
+ 7x = −5
a.7
6 ±
109
6c.
7
3 ±
67
3
b. −7
3 ±
109
3d. −
7
6 ±
22
6
Rewrite the equation in vertex form. Name the vertex and y-intercept.
____ 45. y = x2
− 12x + 34
a. y = (x − 6)2
− 2
vertex: (6, – 2)
y-intercept: (0, 34)
c. y = (x − 12)2
+ 40
vertex: (–12, –2)
y-intercept: (0, –2)
b. y = (x − 12)2
− 2
vertex: (–12, –2)
y-intercept: (0, –2)
d. y = (x − 6)2
+ 70
vertex: (6, – 2)
y-intercept: (0, 34)
Name: ________________________ ID: A
8
Use the Quadratic Formula to solve the equation.
____ 46. −x2
+ 6x − 5 = 0
a. −5, −1 c. −5, 11
b. 1, 5 d. 2, 10
____ 47. −2x2
− 5x + 5 = 0
a. −5
2 ±
65
2c. −
4
5 ±
130
4
b. −5
4 ±
32
2d. −
5
4 ±
65
4
____ 48. 2x2
+ x − 4 = 0
a. −1
2 ±
33
4c. −
1
4 ±
33
4
b. −4 ±66
4d. −
1
2 ±
33
2
____ 49. −4x2
+ x = −4
a. 8 ±65
8c. 8 ±
130
8
b.1
4 ±
65
4d.
1
8 ±
65
8
____ 50. A landscaper is designing a flower garden in the shape of a trapezoid. She wants the shorter base to be 3
yards greater than the height and the longer base to be 7 yards greater than the height. She wants the area to
be 155 square yards. The situation is modeled by the equation h2
+ 5h = 155. Use the Quadratic Formula to
find the height that will give the desired area. Round to the nearest hundredth of a yard.
a. 320 yards c. 20.4 yards
b. 10.2 yards d. 12.7 yards
51. A park planner has sketched a rectangular park in the first quadrant of a coordinate grid. Two sides of the
park lie on the x- and y-axes. A trapezoidal flower bed will be bounded by the line y = x + 7, the x-axis, and
the vertical lines x = 1 and x = a , where a > 1. The area A of the trapezoid is modeled by
A =12
a2
+ 7a −152
. Assume that lengths along the axes are measured in meters. For what value of a will
the trapezoid have an area of 23 square meters? Use the Quadratic Formula to find the answer.
What is the number of real solutions?
____ 52. −x2
+ 9x + 7 = 0
a. one solution c. two solutions
b. no real solutions d. cannot be determined
Name: ________________________ ID: A
9
____ 53.
8x2
− 11x = −3
a. one real solution c. no real solutions
b. two real solutions d. cannot be determined
____ 54. x2
= −7x + 7
a. one solution c. two solutions
b. no real solutions d. cannot be determined
____ 55. −4x2
− 4 = 8x
a. one solution c. no real solutions
b. two solutions d. cannot be determined
____ 56. During a manufacturing process, a metal part in a machine is exposed to varying temperature conditions. The
manufacturer of the machine recommends that the temperature of the machine part remain below 132°F. The
temperature T in degrees Fahrenheit x minutes after the machine is put into operation is modeled by
T = −0.005x2
+ 0.45x + 125. Will the temperature of the part ever reach or exceed 132°F? Use the
discriminant of a quadratic equation to decide.
a. no
b. yes
Simplify the number using the imaginary unit i.
____ 57. −144
a. 12 c. 12i
b. −12 d. 144i
58. −360
Simplify the expression.
____ 59. (3 + i) − (2 − 2i)
a. 1 + 3i c. 4i
b. 5 − i d. −1 − 3i
60. (i)(−7i)
61. (4 − i)(2 + 5i)
62. −2 + i
−4 − 5i
Name: ________________________ ID: A
10
What pair of factors should be used to find the complex solutions for x?
____ 63. 49x2
+ 36 = 0
a. (6x − 7i)(6x + 7i) c. (7x + 6i)(7x + 6i)
b. (6x + 7)(6x + 7) d. (7x + 6i)(7x − 6i)
____ 64. 16x2
+ 4 = 0
a. (4x + 2i)(4x + 2i) c. (4x + 2i)(4x − 2i)
b. (2x + 4)(2x + 4) d. (2x − 4i)(2x + 4i)
____ 65. Find the solutions of the equation.
1
2x
2− x + 5 = 0
a. 1 ± 9 i c. 1 ± 11 i
b. −1 ± 9 i d. −1 ± 11 i
Use graphing to find the solutions to the system of equations.
66. y = x
2+ 7x + 7
y = x + 2
Ï
Ì
Ó
ÔÔÔÔÔÔÔÔÔÔÔÔÔÔ
67. y = −x
2− 4x + 8
y = −x − 2
Ï
Ì
Ó
ÔÔÔÔÔÔÔÔÔÔÔÔÔÔ
What is the solution of the linear-quadratic system of equations?
68. y = x
2+ 7x + 13
y = x + 5
Ï
Ì
Ó
ÔÔÔÔÔÔÔÔÔÔÔÔÔÔ
69. y = x
2+ 3x − 1
y = x + 2
Ï
Ì
Ó
ÔÔÔÔÔÔÔÔÔÔÔÔÔÔ
What is the solution of the quadratic system of equations?
70. y = x
2+ 18x + 35
y = −x2
+ 2x + 5
Ï
Ì
Ó
ÔÔÔÔÔÔÔÔÔÔÔÔÔÔÔ
Name: ________________________ ID: A
11
What is the solution of the system of inequalities?
____ 71.
y ≥ x2
+ 2x + 2
y < −x2
− 4x − 2
Ï
Ì
Ó
ÔÔÔÔÔÔÔÔÔÔÔÔÔÔÔ
a. c.
b. d.
ID: A
1
Algebra 2 Chapter 4
Answer Section
1. ANS:
PTS: 1 DIF: L2 REF: 4-1 Quadratic Functions and Transformations
OBJ: 4-1.1 To identify and graph quadratic functions
NAT: CC A.CED.1| CC F.IF.4| CC F.IF.6| CC F.IF.7| CC F.BF.3| G.2.c| A.2.d
TOP: 4-1 Problem 1 Graphing a Function of the Form f(x)=ax^2
KEY: graphing | quadratic functions
2. ANS:
PTS: 1 DIF: L3 REF: 4-1 Quadratic Functions and Transformations
OBJ: 4-1.1 To identify and graph quadratic functions
NAT: CC A.CED.1| CC F.IF.4| CC F.IF.6| CC F.IF.7| CC F.BF.3| G.2.c| A.2.d
TOP: 4-1 Problem 1 Graphing a Function of the Form f(x)=ax^2
KEY: graphing | quadratic functions
ID: A
2
3. ANS:
f(x) translated up 4 unit(s) and translated to the left 3 unit(s).
PTS: 1 DIF: L3 REF: 4-1 Quadratic Functions and Transformations
OBJ: 4-1.1 To identify and graph quadratic functions
NAT: CC A.CED.1| CC F.IF.4| CC F.IF.6| CC F.IF.7| CC F.BF.3| G.2.c| A.2.d
TOP: 4-1 Problem 2 Graphing Translations of f(x)=x^2
KEY: graphing | quadratic functions | translations
4. ANS: C PTS: 1 DIF: L3
REF: 4-1 Quadratic Functions and Transformations
OBJ: 4-1.1 To identify and graph quadratic functions
NAT: CC A.CED.1| CC F.IF.4| CC F.IF.6| CC F.IF.7| CC F.BF.3| G.2.c| A.2.d
TOP: 4-1 Problem 3 Interpreting Vertex Form
KEY: parabola | vertex form | vertex of a parabola | axis of symmetry
5. ANS: D PTS: 1 DIF: L3
REF: 4-1 Quadratic Functions and Transformations
OBJ: 4-1.1 To identify and graph quadratic functions
NAT: CC A.CED.1| CC F.IF.4| CC F.IF.6| CC F.IF.7| CC F.BF.3| G.2.c| A.2.d
TOP: 4-1 Problem 3 Interpreting Vertex Form
KEY: parabola | vertex form | minimum value | maximum value
6. ANS: A PTS: 1 DIF: L3
REF: 4-1 Quadratic Functions and Transformations
OBJ: 4-1.1 To identify and graph quadratic functions
NAT: CC A.CED.1| CC F.IF.4| CC F.IF.6| CC F.IF.7| CC F.BF.3| G.2.c| A.2.d
TOP: 4-1 Problem 4 Using Vertex Form KEY: parabola | vertex form | graphing | translation
7. ANS:
y = 3(x + 2)2
+ 2
PTS: 1 DIF: L2 REF: 4-1 Quadratic Functions and Transformations
OBJ: 4-1.1 To identify and graph quadratic functions
NAT: CC A.CED.1| CC F.IF.4| CC F.IF.6| CC F.IF.7| CC F.BF.3| G.2.c| A.2.d
TOP: 4-1 Problem 5 Writing a Quadratic Function in Vertex Form
KEY: parabola | equation of a parabola | vertex form
ID: A
3
8. ANS:
y = 3(x + 8)2
− 7
PTS: 1 DIF: L3 REF: 4-1 Quadratic Functions and Transformations
OBJ: 4-1.1 To identify and graph quadratic functions
NAT: CC A.CED.1| CC F.IF.4| CC F.IF.6| CC F.IF.7| CC F.BF.3| G.2.c| A.2.d
TOP: 4-1 Problem 5 Writing a Quadratic Function in Vertex Form
KEY: parabola | vertex form | quadratic function | equation
9. ANS: C PTS: 1 DIF: L3
REF: 4-1 Quadratic Functions and Transformations
OBJ: 4-1.1 To identify and graph quadratic functions
NAT: CC A.CED.1| CC F.IF.4| CC F.IF.6| CC F.IF.7| CC F.BF.3| G.2.c| A.2.d
TOP: 4-1 Problem 5 Writing a Quadratic Function in Vertex Form
KEY: parabola | vertex form | quadratic function | equation
10. ANS: C PTS: 1 DIF: L3
REF: 4-2 Standard Form of a Quadratic Function
OBJ: 4-2.1 To graph quadratic functions written in standard form
NAT: CC A.CED.2| CC F.IF.4| CC F.IF.6| CC F.IF.7| CC F.IF.8| CC F.IF.9| CC F.BF.1
TOP: 4-2 Problem 1 Finding the Features of a Quadratic Function
KEY: standard form | vertex of a parabola | axis of symmetry
11. ANS: C PTS: 1 DIF: L2
REF: 4-2 Standard Form of a Quadratic Function
OBJ: 4-2.1 To graph quadratic functions written in standard form
NAT: CC A.CED.2| CC F.IF.4| CC F.IF.6| CC F.IF.7| CC F.IF.8| CC F.IF.9| CC F.BF.1
TOP: 4-2 Problem 1 Finding the Features of a Quadratic Function
KEY: standard form | minimum value | maximum value
12. ANS:
PTS: 1 DIF: L2 REF: 4-2 Standard Form of a Quadratic Function
OBJ: 4-2.1 To graph quadratic functions written in standard form
NAT: CC A.CED.2| CC F.IF.4| CC F.IF.6| CC F.IF.7| CC F.IF.8| CC F.IF.9| CC F.BF.1
TOP: 4-2 Problem 2 Graphing a Function of the Form y=ax^2+bx+c
KEY: standard form
ID: A
4
13. ANS:
PTS: 1 DIF: L3 REF: 4-2 Standard Form of a Quadratic Function
OBJ: 4-2.1 To graph quadratic functions written in standard form
NAT: CC A.CED.2| CC F.IF.4| CC F.IF.6| CC F.IF.7| CC F.IF.8| CC F.IF.9| CC F.BF.1
TOP: 4-2 Problem 2 Graphing a Function of the Form y=ax^2+bx+c
KEY: standard form
14. ANS:
PTS: 1 DIF: L3 REF: 4-2 Standard Form of a Quadratic Function
OBJ: 4-2.1 To graph quadratic functions written in standard form
NAT: CC A.CED.2| CC F.IF.4| CC F.IF.6| CC F.IF.7| CC F.IF.8| CC F.IF.9| CC F.BF.1
TOP: 4-2 Problem 2 Graphing a Function of the Form y=ax^2+bx+c
KEY: standard form
ID: A
5
15. ANS: C PTS: 1 DIF: L2
REF: 4-2 Standard Form of a Quadratic Function
OBJ: 4-2.1 To graph quadratic functions written in standard form
NAT: CC A.CED.2| CC F.IF.4| CC F.IF.6| CC F.IF.7| CC F.IF.8| CC F.IF.9| CC F.BF.1
TOP: 4-2 Problem 3 Converting Standard Form to Vertex Form
KEY: standard form | vertex form
16. ANS: C PTS: 1 DIF: L2
REF: 4-2 Standard Form of a Quadratic Function
OBJ: 4-2.1 To graph quadratic functions written in standard form
NAT: CC A.CED.2| CC F.IF.4| CC F.IF.6| CC F.IF.7| CC F.IF.8| CC F.IF.9| CC F.BF.1
TOP: 4-2 Problem 3 Converting Standard Form to Vertex Form
KEY: standard form | vertex form
17. ANS: B PTS: 1 DIF: L3
REF: 4-2 Standard Form of a Quadratic Function
OBJ: 4-2.1 To graph quadratic functions written in standard form
NAT: CC A.CED.2| CC F.IF.4| CC F.IF.6| CC F.IF.7| CC F.IF.8| CC F.IF.9| CC F.BF.1
TOP: 4-2 Problem 3 Converting Standard Form to Vertex Form
KEY: standard form | vertex form
18. ANS:
The bridge is about 193.52 ft above the river and the length of the bridge above the arch is about 1250.51 ft
PTS: 1 DIF: L4 REF: 4-2 Standard Form of a Quadratic Function
OBJ: 4-2.1 To graph quadratic functions written in standard form
NAT: CC A.CED.2| CC F.IF.4| CC F.IF.6| CC F.IF.7| CC F.IF.8| CC F.IF.9| CC F.BF.1
TOP: 4-2 Problem 4 Interpreting a Quadratic Graph KEY: standard form
19. ANS: C PTS: 1 DIF: L3
REF: 4-3 Modeling With Quadratic Functions
OBJ: 4-3.1 To model data with quadratic functions NAT: CC F.IF.4| CC F.IF.5| A.2.f
TOP: 4-3 Problem 1 Writing an Equation of a Parabola KEY: quadratic function | quadratic model
20. ANS: C PTS: 1 DIF: L3
REF: 4-3 Modeling With Quadratic Functions
OBJ: 4-3.1 To model data with quadratic functions NAT: CC F.IF.4| CC F.IF.5| A.2.f
TOP: 4-3 Problem 2 Using a Quadratic Model
KEY: quadratic model | quadratic function | word problem | problem solving | multi-part question
21. ANS: B PTS: 1 DIF: L4
REF: 4-3 Modeling With Quadratic Functions
OBJ: 4-3.1 To model data with quadratic functions NAT: CC F.IF.4| CC F.IF.5| A.2.f
TOP: 4-3 Problem 3 Using Quadratic Regression
22. ANS: B PTS: 1 DIF: L3
REF: 4-3 Modeling With Quadratic Functions
OBJ: 4-3.1 To model data with quadratic functions NAT: CC F.IF.4| CC F.IF.5| A.2.f
TOP: 4-3 Problem 3 Using Quadratic Regression
ID: A
6
23. ANS:
(x − 5)(x − 10)
PTS: 1 DIF: L2 REF: 4-4 Factoring Quadratic Expressions
OBJ: 4-4.1 To find common and binomial factors of quadratic expressions
NAT: CC A.SSE.2| N.5.c| A.2.a TOP: 4-4 Problem 1 Factoring ax^2+bx+c when a=+/-1
KEY: factoring | quadratic expression
24. ANS:
−(x − 8)(x + 4)
PTS: 1 DIF: L3 REF: 4-4 Factoring Quadratic Expressions
OBJ: 4-4.1 To find common and binomial factors of quadratic expressions
NAT: CC A.SSE.2| N.5.c| A.2.a TOP: 4-4 Problem 1 Factoring ax^2+bx+c when a=+/-1
KEY: factoring | quadratic expression
25. ANS: −5x(2x + 3)
PTS: 1 DIF: L2 REF: 4-4 Factoring Quadratic Expressions
OBJ: 4-4.1 To find common and binomial factors of quadratic expressions
NAT: CC A.SSE.2| N.5.c| A.2.a TOP: 4-4 Problem 2 Finding Common Factors
KEY: factoring | greatest common factor
26. ANS: 2(x + 3)(x + 5)
PTS: 1 DIF: L3 REF: 4-4 Factoring Quadratic Expressions
OBJ: 4-4.1 To find common and binomial factors of quadratic expressions
NAT: CC A.SSE.2| N.5.c| A.2.a TOP: 4-4 Problem 2 Finding Common Factors
KEY: factoring | greatest common factor
27. ANS: −4(x − 4)(x + 2)
PTS: 1 DIF: L3 REF: 4-4 Factoring Quadratic Expressions
OBJ: 4-4.1 To find common and binomial factors of quadratic expressions
NAT: CC A.SSE.2| N.5.c| A.2.a TOP: 4-4 Problem 2 Finding Common Factors
KEY: factoring | greatest common factor
28. ANS: (3x + 5)(x + 7)
PTS: 1 DIF: L3 REF: 4-4 Factoring Quadratic Expressions
OBJ: 4-4.1 To find common and binomial factors of quadratic expressions
NAT: CC A.SSE.2| N.5.c| A.2.a TOP: 4-4 Problem 3 Factoring ax^2+bx+c when abs(a) not = 1
KEY: factoring
29. ANS:
(4x − 5)2
PTS: 1 DIF: L3 REF: 4-4 Factoring Quadratic Expressions
OBJ: 4-4.2 To factor special quadratic expressions NAT: CC A.SSE.2| N.5.c| A.2.a
TOP: 4-4 Problem 4 Factoring a Perfect Square Trinomial KEY: factoring | perfect square trinomial
ID: A
7
30. ANS:
(5x + 3)(5x − 3)
PTS: 1 DIF: L2 REF: 4-4 Factoring Quadratic Expressions
OBJ: 4-4.2 To factor special quadratic expressions NAT: CC A.SSE.2| N.5.c| A.2.a
TOP: 4-4 Problem 5 Factoring a Difference of Two Squares KEY: difference of two squares | factoring
31. ANS:
x2
+ 2xy + y2
PTS: 1 DIF: L2 REF: 4-4 Factoring Quadratic Expressions
OBJ: 4-4.2 To factor special quadratic expressions NAT: CC A.SSE.2| N.5.c| A.2.a
TOP: 4-4 Problem 5 Factoring a Difference of Two Squares KEY: identify ways to rewrite expressions
32. ANS:
–4, –7
PTS: 1 DIF: L2 REF: 4-5 Quadratic Equations
OBJ: 4-5.1 To solve quadratic equations by factoring
NAT: CC A.SSE.1.a| CC A.APR.3| CC A.CED.1| A.2.a| A.4.a| A.4.c
TOP: 4-5 Problem 1 Solving a Quadratic Equation by Factoring
KEY: Zero-Product Property
33. ANS:
–6, −7
3
PTS: 1 DIF: L3 REF: 4-5 Quadratic Equations
OBJ: 4-5.1 To solve quadratic equations by factoring
NAT: CC A.SSE.1.a| CC A.APR.3| CC A.CED.1| A.2.a| A.4.a| A.4.c
TOP: 4-5 Problem 1 Solving a Quadratic Equation by Factoring
KEY: Zero-Product Property
34. ANS:
5.51 seconds
PTS: 1 DIF: L2 REF: 4-5 Quadratic Equations
OBJ: 4-5.1 To solve quadratic equations by factoring
NAT: CC A.SSE.1.a| CC A.APR.3| CC A.CED.1| A.2.a| A.4.a| A.4.c
TOP: 4-5 Problem 4 Using a Quadratic Equation
35. ANS:
The frog jumped about 22.92 ft far and about 3.15 ft high.
PTS: 1 DIF: L3 REF: 4-5 Quadratic Equations
OBJ: 4-5.1 To solve quadratic equations by factoring
NAT: CC A.SSE.1.a| CC A.APR.3| CC A.CED.1| A.2.a| A.4.a| A.4.c
TOP: 4-5 Problem 4 Using a Quadratic Equation
ID: A
8
36. ANS:
a bridge
PTS: 1 DIF: L3 REF: 4-5 Quadratic Equations
OBJ: 4-5.1 To solve quadratic equations by factoring
NAT: CC A.SSE.1.a| CC A.APR.3| CC A.CED.1| A.2.a| A.4.a| A.4.c
TOP: 4-5 Problem 4 Using a Quadratic Equation
37. ANS:
7 , – 7
PTS: 1 DIF: L2 REF: 4-6 Completing the Square
OBJ: 4-6.1 To solve equations by completing the square NAT: CC A.REI.4.b| A.2.a| A.4.c| A.4.g
TOP: 4-6 Problem 1 Solving by Finding Square Roots
38. ANS:
−7
6,
7
6
PTS: 1 DIF: L3 REF: 4-6 Completing the Square
OBJ: 4-6.1 To solve equations by completing the square NAT: CC A.REI.4.b| A.2.a| A.4.c| A.4.g
TOP: 4-6 Problem 1 Solving by Finding Square Roots
39. ANS: A PTS: 1 DIF: L3 REF: 4-6 Completing the Square
OBJ: 4-6.1 To solve equations by completing the square NAT: CC A.REI.4.b| A.2.a| A.4.c| A.4.g
TOP: 4-6 Problem 2 Determining Dimensions
40. ANS: B PTS: 1 DIF: L3 REF: 4-6 Completing the Square
OBJ: 4-6.1 To solve equations by completing the square NAT: CC A.REI.4.b| A.2.a| A.4.c| A.4.g
TOP: 4-6 Problem 2 Determining Dimensions
41. ANS: B PTS: 1 DIF: L3 REF: 4-6 Completing the Square
OBJ: 4-6.1 To solve equations by completing the square NAT: CC A.REI.4.b| A.2.a| A.4.c| A.4.g
TOP: 4-6 Problem 3 Solving a Perfect Square Trinomial Equation
42. ANS: C PTS: 1 DIF: L2 REF: 4-6 Completing the Square
OBJ: 4-6.1 To solve equations by completing the square NAT: CC A.REI.4.b| A.2.a| A.4.c| A.4.g
TOP: 4-6 Problem 3 Solving a Perfect Square Trinomial Equation
43. ANS: D PTS: 1 DIF: L3 REF: 4-6 Completing the Square
OBJ: 4-6.1 To solve equations by completing the square NAT: CC A.REI.4.b| A.2.a| A.4.c| A.4.g
TOP: 4-6 Problem 5 Solving by Completing the Square KEY: completing the square
44. ANS: A PTS: 1 DIF: L3 REF: 4-6 Completing the Square
OBJ: 4-6.1 To solve equations by completing the square NAT: CC A.REI.4.b| A.2.a| A.4.c| A.4.g
TOP: 4-6 Problem 5 Solving by Completing the Square KEY: completing the square
45. ANS: A PTS: 1 DIF: L3 REF: 4-6 Completing the Square
OBJ: 4-6.2 To rewrite functions by completing the square NAT: CC A.REI.4.b| A.2.a| A.4.c| A.4.g
TOP: 4-6 Problem 6 Writing in Vertex Form
46. ANS: B PTS: 1 DIF: L2 REF: 4-7 The Quadratic Formula
OBJ: 4-7.1 To solve quadratic equations using the Quadratic Formula
NAT: CC A.REI.4.b| A.2.a| A.4.c| A.4.e| A.4.f
TOP: 4-7 Problem 1 Using the Quadratic Formula KEY: Quadratic Formula
ID: A
9
47. ANS: D PTS: 1 DIF: L3 REF: 4-7 The Quadratic Formula
OBJ: 4-7.1 To solve quadratic equations using the Quadratic Formula
NAT: CC A.REI.4.b| A.2.a| A.4.c| A.4.e| A.4.f
TOP: 4-7 Problem 1 Using the Quadratic Formula KEY: Quadratic Formula
48. ANS: C PTS: 1 DIF: L3 REF: 4-7 The Quadratic Formula
OBJ: 4-7.1 To solve quadratic equations using the Quadratic Formula
NAT: CC A.REI.4.b| A.2.a| A.4.c| A.4.e| A.4.f
TOP: 4-7 Problem 1 Using the Quadratic Formula KEY: Quadratic Formula
49. ANS: D PTS: 1 DIF: L3 REF: 4-7 The Quadratic Formula
OBJ: 4-7.1 To solve quadratic equations using the Quadratic Formula
NAT: CC A.REI.4.b| A.2.a| A.4.c| A.4.e| A.4.f
TOP: 4-7 Problem 1 Using the Quadratic Formula KEY: Quadratic Formula
50. ANS: B PTS: 1 DIF: L3 REF: 4-7 The Quadratic Formula
OBJ: 4-7.1 To solve quadratic equations using the Quadratic Formula
NAT: CC A.REI.4.b| A.2.a| A.4.c| A.4.e| A.4.f
TOP: 4-7 Problem 2 Applying the Quadratic Formula KEY: Quadratic Formula
51. ANS:
110 − 7 meters, or about 3.49
PTS: 1 DIF: L4 REF: 4-7 The Quadratic Formula
OBJ: 4-7.1 To solve quadratic equations using the Quadratic Formula
NAT: CC A.REI.4.b| A.2.a| A.4.c| A.4.e| A.4.f
TOP: 4-7 Problem 2 Applying the Quadratic Formula KEY: Quadratic Formula
52. ANS: C PTS: 1 DIF: L2 REF: 4-7 The Quadratic Formula
OBJ: 4-7.2 To determine the number of solutions by using the discriminant
NAT: CC A.REI.4.b| A.2.a| A.4.c| A.4.e| A.4.f
TOP: 4-7 Problem 3 Using the Discriminant KEY: discriminant | Quadratic Formula
53. ANS: B PTS: 1 DIF: L2 REF: 4-7 The Quadratic Formula
OBJ: 4-7.2 To determine the number of solutions by using the discriminant
NAT: CC A.REI.4.b| A.2.a| A.4.c| A.4.e| A.4.f
TOP: 4-7 Problem 3 Using the Discriminant KEY: discriminant | Quadratic Formula
54. ANS: A PTS: 1 DIF: L2 REF: 4-7 The Quadratic Formula
OBJ: 4-7.2 To determine the number of solutions by using the discriminant
NAT: CC A.REI.4.b| A.2.a| A.4.c| A.4.e| A.4.f
TOP: 4-7 Problem 3 Using the Discriminant KEY: discriminant | Quadratic Formula
55. ANS: A PTS: 1 DIF: L2 REF: 4-7 The Quadratic Formula
OBJ: 4-7.2 To determine the number of solutions by using the discriminant
NAT: CC A.REI.4.b| A.2.a| A.4.c| A.4.e| A.4.f
TOP: 4-7 Problem 3 Using the Discriminant KEY: discriminant | Quadratic Formula
56. ANS: B PTS: 1 DIF: L3 REF: 4-7 The Quadratic Formula
OBJ: 4-7.2 To determine the number of solutions by using the discriminant
NAT: CC A.REI.4.b| A.2.a| A.4.c| A.4.e| A.4.f
TOP: 4-7 Problem 4 Using the Discriminant to Solve a Problem
KEY: discriminant | Quadratic Formula
57. ANS: C PTS: 1 DIF: L2 REF: 4-8 Complex Numbers
OBJ: 4-8.1 To identify, graph, and perform operations with complex numbers
NAT: CC N.CN.1| CC N.CN.2| CC N.CN.7| CC N.CN.8| N.5.f| A.4.g
TOP: 4-8 Problem 1 Simplifying a Number using i KEY: imaginary number | imaginary unit
ID: A
10
58. ANS:
6i 10
PTS: 1 DIF: L2 REF: 4-8 Complex Numbers
OBJ: 4-8.1 To identify, graph, and perform operations with complex numbers
NAT: CC N.CN.1| CC N.CN.2| CC N.CN.7| CC N.CN.8| N.5.f| A.4.g
TOP: 4-8 Problem 1 Simplifying a Number using i KEY: imaginary number | imaginary unit
59. ANS: A PTS: 1 DIF: L3 REF: 4-8 Complex Numbers
OBJ: 4-8.1 To identify, graph, and perform operations with complex numbers
NAT: CC N.CN.1| CC N.CN.2| CC N.CN.7| CC N.CN.8| N.5.f| A.4.g
TOP: 4-8 Problem 3 Adding and Subtracting Complex Numbers
KEY: complex number
60. ANS:
7
PTS: 1 DIF: L2 REF: 4-8 Complex Numbers
OBJ: 4-8.1 To identify, graph, and perform operations with complex numbers
NAT: CC N.CN.1| CC N.CN.2| CC N.CN.7| CC N.CN.8| N.5.f| A.4.g
TOP: 4-8 Problem 4 Multiplying Complex Numbers KEY: complex number
61. ANS:
(13 + 18i)
PTS: 1 DIF: L3 REF: 4-8 Complex Numbers
OBJ: 4-8.1 To identify, graph, and perform operations with complex numbers
NAT: CC N.CN.1| CC N.CN.2| CC N.CN.7| CC N.CN.8| N.5.f| A.4.g
TOP: 4-8 Problem 4 Multiplying Complex Numbers KEY: complex number
62. ANS:
3
41−
14
41i
PTS: 1 DIF: L3 REF: 4-8 Complex Numbers
OBJ: 4-8.1 To identify, graph, and perform operations with complex numbers
NAT: CC N.CN.1| CC N.CN.2| CC N.CN.7| CC N.CN.8| N.5.f| A.4.g
TOP: 4-8 Problem 5 Dividing Complex Numbers
KEY: complex number | complex conjugates
63. ANS: D PTS: 1 DIF: L2 REF: 4-8 Complex Numbers
OBJ: 4-8.2 To find complex number solutions of quadratic equations
NAT: CC N.CN.1| CC N.CN.2| CC N.CN.7| CC N.CN.8| N.5.f| A.4.g
TOP: 4-8 Problem 6 Factoring using Complex Conjugates KEY: complex conjugates
64. ANS: C PTS: 1 DIF: L2 REF: 4-8 Complex Numbers
OBJ: 4-8.2 To find complex number solutions of quadratic equations
NAT: CC N.CN.1| CC N.CN.2| CC N.CN.7| CC N.CN.8| N.5.f| A.4.g
TOP: 4-8 Problem 6 Factoring using Complex Conjugates KEY: complex conjugates
65. ANS: A PTS: 1 DIF: L3 REF: 4-8 Complex Numbers
OBJ: 4-8.2 To find complex number solutions of quadratic equations
NAT: CC N.CN.1| CC N.CN.2| CC N.CN.7| CC N.CN.8| N.5.f| A.4.g
TOP: 4-8 Problem 7 Finding Imaginary Solutions
KEY: complex number | imaginary number
ID: A
11
66. ANS:
(–5, –3)
(–1, 1)
PTS: 1 DIF: L2 REF: 4-9 Quadratic Systems
OBJ: 4-9.1 To solve and graph systems of linear and quadratic equations
NAT: CC A.CED.3| CC A.REI.7| A.4.a| A.4.d
TOP: 4-9 Problem 1 Solving a Linear-Quadratic System by Graphing
67. ANS:
(–5, 3)
(2, –4)
PTS: 1 DIF: L2 REF: 4-9 Quadratic Systems
OBJ: 4-9.1 To solve and graph systems of linear and quadratic equations
NAT: CC A.CED.3| CC A.REI.7| A.4.a| A.4.d
TOP: 4-9 Problem 1 Solving a Linear-Quadratic System by Graphing
ID: A
12
68. ANS:
(–4, 1)
(–2, 3)
PTS: 1 DIF: L2 REF: 4-9 Quadratic Systems
OBJ: 4-9.1 To solve and graph systems of linear and quadratic equations
NAT: CC A.CED.3| CC A.REI.7| A.4.a| A.4.d
TOP: 4-9 Problem 1 Solving a Linear-Quadratic System by Graphing
69. ANS:
(1, 3)
(–3, –1)
PTS: 1 DIF: L3 REF: 4-9 Quadratic Systems
OBJ: 4-9.1 To solve and graph systems of linear and quadratic equations
NAT: CC A.CED.3| CC A.REI.7| A.4.a| A.4.d
TOP: 4-9 Problem 1 Solving a Linear-Quadratic System by Graphing
70. ANS:
(–3, –10)
(–5, –30)
PTS: 1 DIF: L3 REF: 4-9 Quadratic Systems
OBJ: 4-9.1 To solve and graph systems of linear and quadratic equations
NAT: CC A.CED.3| CC A.REI.7| A.4.a| A.4.d
TOP: 4-9 Problem 3 Solving a Quadratic System of Equations
71. ANS: C PTS: 1 DIF: L3 REF: 4-9 Quadratic Systems
OBJ: 4-9.1 To solve and graph systems of linear and quadratic equations
NAT: CC A.CED.3| CC A.REI.7| A.4.a| A.4.d
TOP: 4-9 Problem 4 Solving a Quadratic System of Inequalities
ID: A Algebra 2 Chapter 4 [Answer Strip]
_____ 4.C
_____ 5.D
_____ 6.A _____ 9.C
_____ 10.C
_____ 11.C
_____ 15.C
_____ 16.C
_____ 17.B
_____ 19.C
_____ 20.C
_____ 21.B
_____ 22.B
ID: A Algebra 2 Chapter 4 [Answer Strip]
_____ 39.A
_____ 40.B
_____ 41.B
_____ 42.C
_____ 43.D
_____ 44.A
_____ 45.A
_____ 46.B
_____ 47.D
_____ 48.C
_____ 49.D
_____ 50.B
_____ 52.C
_____ 53.B
_____ 54.A
_____ 55.A
_____ 56.B
_____ 57.C
_____ 59.A
_____ 63.D
_____ 64.C
_____ 65.A
_____ 71.C