Quadratics Unit: Classwork & Homework
Characteristics of Quadratics
Class Work
If the following equation is a quadratic, write the equation in standard form.
1. y= 2 + 3x2 – 5
2. 4x – 5 = x + y
3. 5x +4y= x2 – 2
4. 4x2 – 2 = 4x
5. 3x2 + 2x = 3x2 – 6
For each of the following graphs, find the direction the parabola opens, the vertex, state whether the vertex is a
maximum or minimum, the domain, the range, the axis of symmetry, and the x-intercepts, if any exist.
6.
7.
x scale is 1
x scale is 1
y scale is 2
y scale is 2
y
y
8
8
6
6
4
4
2
x
-9
-8
-7
-6
-5
-4
-3
-2
-1
1
2
3
4
5
6
7
8
2
9
x
-2
-9
-8
-7
-6
-5
-4
-3
-2
-1
1
2
3
4
5
6
7
8
9
-4
-2
-6
-4
-8
-6
-8
Homework
If the following equation is a quadratic, write the equation in standard form.
8. y= 7 + 3x – 5
9. 4x – 6 = x2 + y
10. 10x +2y= 8x2 – 2
11. 4x2 – 2 +10x = 4x
12. 3x2 - 2x = 2x2 – 7
For each of the following graphs, find the direction the parabola opens, the vertex, state whether the vertex is a
maximum or minimum, the domain, the range, the axis of symmetry, and the x-intercepts, if any exist.
13.
14.
x scale is 1
x scale is 1
y scale is 2
y scale is 2
y
y
8
8
6
6
4
4
2
x
2
-9
-8
-7
-6
-5
-4
x
-9
-8
-7
-6
-5
-4
-3
-2
-1
1
2
3
4
5
6
7
8
-3
-2
-1
1
2
3
4
5
6
7
8
9
-2
9
-4
-2
-6
-4
-8
-6
-8
Algebra II - Quadratics
~1~
NJCTL.org
Identifying Parts of a Parabola
Class Work
Find the axis of symmetry, the vertex, and the y-intercept of each parabola. Graph the quadratic.
15. y= x2 + 2x + 1
16. y= x2 - 6x + 8
17. y= x2 - 4x - 2
18. y= 2x2 + 6x + 3
19. y= 3x2 - 4x - 2
Without graphing, does the graph of the given equation open up or down? Is the graph wider or narrower than the
parent equation of y=x2? What is the y-intercept?
20.
21.
22.
23.
24.
f(x) = 2x2 +3x -4
y = -.7x2 -4x +3
y = -1.2x2 +6
g(x) = 3x2 +3x
y = -4x2
Homework
Find the axis of symmetry, the vertex, and the y-intercept of each parabola. Graph the quadratic.
25. y= x2 + 2x - 8
26. y= x2 - 4x + 3
27. y= .5x2 + 3x - 8
28. y= x2 + 7x + 6
29. y= 3x2 - 4x
Without graphing, does the graph of the given equation open up or down? Is the graph wider or narrower than the parent
equation of y=x2? What is the y-intercept?
30.
31.
32.
33.
34.
f(x) =-.6x2 +3x -6
y = 1.7x2 -4x +5
y = -1.02x2 +8
g(x) = 1.3x2 +4x
y = 5x2
Algebra II - Quadratics
~2~
NJCTL.org
Transformations
Class Work
In each exercise the function is given. Describe the transformation of the parent function. Graph the function.
35. 𝑓(𝑥) = 𝑥 2 + 4
36. 𝑔(𝑥) = 𝑥 2 − 2
37. 𝑓(𝑥) = (𝑥 − 2)2
38. 𝑔(𝑥) = (𝑥 + 3)2
39. 𝑓(𝑥) = −𝑥 2
40. 𝑔(𝑥) = (−𝑥)2
Home Work
In each exercise the function is given. Describe the transformation of the parent function. Graph the function.
41. 𝑓(𝑥) = 3𝑥 2
42. 𝑔(𝑥) = (2𝑥)2
1
43. 𝑓(𝑥) = ( 𝑥)
2
2
44. 𝑔(𝑥) = . 3𝑥 2
45. 𝑓(𝑥) = −2(𝑥 + 1)2
46. 𝑔(𝑥) = (𝑥 − 3)2 + 4
Graphing to Find Zeros
Class Work
Find the zeros of the following quadratics:
47.
y
8
6
4
2
x
-9
-8
-7
-6
-5
-4
-3
-2
-1
1
2
3
4
5
6
7
8
9
5
6
-2
-4
-6
-8
y
8
6
48.
4
2
x
-9
-8
-7
-6
-5
-4
-3
-2
-1
1
2
3
4
7
8
9
-2
-4
-6
-8
Algebra II - Quadratics
~3~
NJCTL.org
Find the zeros of the following quadratics by graphing.
49. y = x2 -4x +3
50. h(x) = -x2 +3x -8
51. y = -x2 -8x -15
52. y = -x2 -8x -16
53. f(x) = x2 +3x -10
54. g(x) = 2x2 +4x +2
55. y = -3x2 +4x +4
Homework
Find the zeros of the following quadratics:
56.
y
8
6
4
2
x
-9
-8
-7
-6
-5
-4
-3
-2
-1
1
2
3
4
5
6
7
8
9
-2
-4
-6
-8
y
8
6
4
2
57.
x
-9
-8
-7
-6
-5
-4
-3
-2
-1
1
2
3
4
5
6
7
8
9
-2
-4
-6
-8
Find the zeros of the following quadratics by graphing.
58. y = x2 -6x +5
59. y = -x2 +3x +10
60. y = x2 +6x +9
61. f(x) = x2 +x -12
62. y = x2 +2x +4
63. g(x) = 2x2 +5x +2
64. y = -3x2 +11x +4
Algebra II - Quadratics
~4~
NJCTL.org
Solving by Factoring
Class Work
Solve the following quadratics by factoring.
65. a2 +4a +3= 0
70. f2 +4f +4 = 0
66. b2 -4b -5= 0
71. –g2 +5g = 6
67. -c2 -6c = -7
72. 2h2 +7h +6= 0
68. d2 +8d = -12
73. 3j2 -4j = -1
69. -e2 +9 = 0
Home Work
Solve the following quadratics by factoring.
74. a2 +6a +5= 0
79. f2 +6f +9 = 0
75. b2 -b -6= 0
80. –g2 +7g = 6
76. -c2 -6c = 8
81. 2h2 +8h +6= 0
77. d2 +7d = -10
82. 3j2 -7j = -4
78. -e2 +16 = 0
Solving Using the Square Roots Method
Class Work Solve the following quadratics using the square roots method.
83. m2 = 16
86. 5q2 = 80
84. n2 = 25
87. r2 -3 =6
85. 3p2 = 12
Algebra II - Quadratics
~5~
NJCTL.org
88. s2 +8 =17
91. (v -7)2 -5 = 11
89. 2t2 -6 = -4
92. 2(w -3)2 +6 = 56
90. 3u2 +5 = 17
93. The square of six less than a number is twenty-five. Write an equation that models this situation. Solve the
equation.
Homework Solve the following quadratics using the square roots method.
94. m2 = 36
99. s2 +8 = 24
95. n2 = 64
100.
2t2 -6 = 12
96. 3p2 = 27
101.
3u2 +5 = 8
97. 5q2 = 20
102.
(v -2)2 +4 = 13
98. r2 -3 = 13
103.
3(w +4)2 -4 = 44
104.
Two times the square of five more than a number is seventy-two. Write an equation that models this
situation. Solve the equation.
Solving by Completing the Square
Class Work
Fill in the blank to complete the square.
105.
a2 + 8a +__
106.
b2 + 10b +__
107.
c2 - 4c +__
108.
d2 - 6d +__
109.
e2 + 7e +__
Algebra II - Quadratics
~6~
NJCTL.org
f2 - 5f +__
110.
Solve the following quadratics by completing the square.
111.
h2 + 6h =16
112.
j2 - 8j = -7
113.
k2 + 9 = -10k
114.
m2 - 13 = 12m
115.
14n + 20 = -n2
116.
8p + p2 = 0
117.
2q2 - 8q = 40
118.
3r2 + 27r = 12
119.
A toy rocket launched into the air has a height (h feet) at any given time (t seconds) as h = -16t2 + 96t
until it hits the ground. At what time(s) is it at a height of 7 feet above the ground?
Homework
Fill in the blank to complete the square.
120.
a2 + 12a +__
121.
b2 + b +__
122.
c2 - 14c +__
123.
d2 - 16d +__
124.
e2 + 9e +__
125.
f2 - 1f +__
Solve the following quadratics by completing the square.
126.
h2 + 4h =12
127.
j2 - 10j = -9
128.
k2 + 15 = -14k
129.
m2 - 21 = 20m
130.
2n - 80= -n2
131.
6p + p2 = 0
132.
2q2 - 12q = -22
133.
3r2 + 15r = 18
134.
h=
A toy rocket launched into the air has a height (h feet) at any given time (t seconds) as
-16t2
+ 160t until it hits the ground. At what time(s) is it at a height of 9 feet above the ground?
Complex Numbers
Classwork
Complete each of the following operations with complex numbers. Simplify as much as possible.
135.
𝑖 + 6𝑖
136.
−1 − 8𝑖 − 4 − 𝑖
137.
−3 + 6𝑖 − (−5 − 3𝑖) − 8𝑖
138.
4𝑖(−2 − 8𝑖)
Algebra II - Quadratics
~7~
NJCTL.org
139.
(−2 − 𝑖)(4 + 𝑖)
140.
(1 − 7𝑖)2
141.
(8 − 3𝑖)(8 + 3𝑖)
142.
143.
144.
1−9𝑖
2𝑖
4−7𝑖
3+8𝑖
5+2𝑖
4−11𝑖
Homework
145.
−8𝑖 − 7𝑖
146.
7+𝑖+4+4
147.
3 + 3𝑖 + 8 − 2𝑖 − 7
148.
−3𝑖(4 − 10𝑖)
149.
(8 − 6𝑖)(−4 − 4𝑖)
150.
(8 − 3𝑖)2
151.
(−2 − 2𝑖)(7 + 8𝑖)
152.
153.
154.
8−4𝑖
5𝑖
1−6𝑖
7−2𝑖
9+2𝑖
3+𝑖
Solving Using the Quadratic Formula
Class Work
Solve the following using the quadratic formula. Leave irrational answers in radical form.
155.
x2 +8x -6 =0
156.
g2 -4g +2 =0
157.
3d2 + 4d -3 =0
158.
-2m2 + 3m = 1
159.
4w2 -8 = 5w
160.
7z – 9z2 = -4
Algebra II - Quadratics
~8~
NJCTL.org
161.
An employee makes (2x + 3) dollars an hour for x hours. If the employer wants to pay no more than $120
a day, what is the maximum number of hours the employee can work? (Round to the nearest quarter hour)
Homework
Solve the following using the quadratic formula. Leave irrational answers in radical form.
162.
x2 +7x -5 =0
163.
g2 -5g +3 =0
164.
2d2 + 5d -3 =0
165.
-3m2 + 4m = -5
166.
5w2 -2 = 5w
167.
3z – 6z2 = -8
168.
An employee makes (3x - 5) dollars an hour for x hours. If the employer wants to pay no more than $200
a day, what is the maximum number of hours the employee can work? (Round to the nearest quarter hour)
Discriminant
Class Work
Find the discriminant for each quadratic equation. State the number of real roots and then find the real solution(s), if any
exist.
169.
x2 - 6x + 5 = 0
170.
2x2 - 4x - 6 = 0
171.
3x + 4x2 + 5 = 0
172.
6x – 9 = x2
173.
3x2 = 6x – 8
174.
4x2 - 9x – 2= 0
Algebra II - Quadratics
~9~
NJCTL.org
175.
x (2x – 5) = 10
176.
A rock is thrown with a height equation of h = -16t2 + 20t + 5 (where h is the height of the rock in feet at
any given time of t in seconds). Will it reach a height of 30 feet? Explain your answer.
Homework
Find the discriminant for each quadratic equation. State the number of real roots and then find the real solution(s), if any
exist.
177.
3x2 - 9x + 7 = 0
178.
2x2 - 4x + 2 = 0
179.
5x + 7x2 + 8 = 0
180.
7x – 6 = 2x2
181.
5x2 = 7x – 6
182.
3x2 - 7x – 8= 0
183.
(x + 3)(2x + 6) = 11
184.
A rock is thrown with a height equation of h = -16t2 + 64t + 5 (where h is the height of the rock in feet at
any given time of t in seconds). Will it reach a height of 50 feet? Explain your answer.
Vertex Form of a Parabola
Class Work
Find the vertex, direction of openness, and axis of symmetry for each of the following.
185.
𝑦 = 1(𝑥 − 2)2 + 10
186.
𝑦 = −2(𝑥 + 5)2 − 4
187.
𝑦 = − (𝑥 − 6)2 + 8
188.
𝑦 = 2(𝑥 + 7)2
189.
𝑦 = 7(𝑥 − 3)2 + 4
190.
𝑦 = −3(𝑥 + 2)2 − 5
191.
𝑦=
192.
𝑦 = 4(𝑥)2 − 4
6
5
7
−11
(𝑥 − 4)2 + 6
Convert the following equations from standard form to vertex form.
193.
𝑦 = 𝑥 2 + 6𝑥 + 2
194.
𝑦 = 𝑥 2 − 10𝑥 + 20
Algebra II - Quadratics
~10~
NJCTL.org
195.
𝑦 = 𝑥 2 + 8𝑥 − 12
196.
𝑦 = 𝑥 2 + 5𝑥 + 3
197.
𝑦 = 𝑥2 + 𝑥 − 1
198.
𝑦 = 𝑥 2 + 4𝑥 + 4
199.
𝑦 = 3𝑥 2 + 6𝑥 − 2
200.
𝑦 = 2𝑥 2 − 12𝑥 − 4
201.
𝑦 = −6𝑥 2 + 12𝑥 + 2
202.
𝑦 = −5𝑥 2 − 10𝑥 − 3
Homework
Find the vertex, direction of openness, and axis of symmetry for each of the following.
203.
𝑦 = −2(𝑥 − 3)2 + 1
204.
𝑦 = 3(𝑥 + 6)2
205.
𝑦 = − (𝑥 + 4)2 + 1
206.
𝑦 = 4(𝑥 − 8)2 + 11
207.
𝑦 = −(𝑥 + 2)2 − 3
208.
𝑦 = −5(𝑥 + 1)2 − 2
209.
𝑦 = 3(𝑥 − 3)2 + 8
210.
𝑦 = 2(𝑥)2 − 3
7
2
Convert the following equations from standard form to vertex form.
211.
𝑦 = 𝑥 2 + 8𝑥 + 2
212.
𝑦 = 𝑥 2 − 12𝑥 + 20
213.
𝑦 = 𝑥 2 + 4𝑥 − 12
214.
𝑦 = 𝑥 2 + 3𝑥 + 3
215.
𝑦 = 𝑥 2 + 7𝑥 − 1
216.
𝑦 = 𝑥 2 + 6𝑥 + 9
217.
𝑦 = 4𝑥 2 + 12𝑥 − 2
218.
𝑦 = −6𝑥 2 + 24𝑥 − 4
219.
𝑦 = 3𝑥 2 − 18𝑥 + 2
220.
𝑦 = −2𝑥 2 − 10𝑥 − 3
Mixed Application Problems
Class Work
Solve the following problems using any method.
221.
The product of two consecutive positive integers is 272, find the integers.
222.
The product of two consecutive positive even integers is 528, find the integers.
223.
The product of two consecutive odd integers is 255, find the integers.
Algebra II - Quadratics
~11~
NJCTL.org
224.
Two planes leave airport at the same time (from different runways), one traveling south and one
starveling west. If three hours later they are 500 miles apart and the plane flying south has traveled 200 miles
farther, how far did the one flying west travel?
225.
Two cars leave a gas station at the same time, one traveling north and one traveling east. One hour later
they are 80 miles apart and the one traveling east went 10 miles farther, how far is it from the gas station?
226.
A square has its length increased by 4 feet and its width by 5 feet. If the resulting rectangle has an area
of 132 square feet what was the perimeter of the original square?
227.
A rectangular parking lot has a width 30 feet more than its length. The owners are able to increase the
width by 20 feet and the length by 40. The new lot has an area of 27,200 square feet, what is the area of the
original lot?
228.
A square’s sides are tripled producing an area of 81 square feet. What is the ratio of the area of the
original square to the transformed square?
229.
A garden has a length of (x + 2) feet and a width of (2x - 1) feet. The garden’s total area is 88 square
feet. Find the length.
Homework
Solve the following problems using any method.
230.
The product of two consecutive positive integers is 342, find the integers.
231.
The product of two consecutive positive even integers is 168, find the integers.
232.
The product of two consecutive positive odd integers is 483, find the integers.
233.
Two planes leave airport at the same time (from different runways), one traveling south and one traveling
west. If three hours later they are 600 miles apart and the plane flying south has traveled 100 miles farther, how
far did the one flying west travel?
234.
Two cars leave a gas station at the same time, one traveling north and one traveling east. One hour later
they are 90 miles apart and the one traveling east went 15 miles farther, how far is it from the gas station?
235.
A square has its length increased by 6 feet and its width by 8 feet. If the resulting rectangle has an area
of 239.25 square feet what was the perimeter of the original square?
236.
A rectangular parking lot has a width 20 feet more than its length. The owners are able to increase the
width by 20 feet and the length by 40. The new lot has an area of 7225 square feet, what is the area of the
original lot?
Algebra II - Quadratics
~12~
NJCTL.org
237.
A square’s sides are quadrupled producing an area of 64 square feet. What is the ratio of the area of the
original square to the transformed square?
238.
A garden has a length of (x - 4)feet and a width of (2x +3)feet. The garden’s total area is 76 square feet.
Find the length.
End of Unit Review: Multiple Choice
1. Comparing the graph of y = 2x2 + 6x -3/2 to its parent function, it:
A) opens down and is wider than the parent function graph.
B) opens down and is narrower than the parent function graph.
C) opens up and is wider than the parent function graph.
D) opens up and is narrower than the parent function graph.
2. What is the equation of the axis of symmetry of y = 3x2 + 6x – 7?
A) x = -6
B) x = -1
C) x = 1
D) x = 6
3. What is the coordinates of the vertex of y = 3x2 + 6x – 7?
A) (-6 , 65)
B) (-1 , -10)
C) (1 , -14)
D) (6 , 137)
4. What is the y- intercept of y = 3x2 + 6x – 7
A) (0 , 7)
B) (7 , 0)
C) (0 , -7)
D) (-7, 0)
5. Which graph to the right has no zeros?
A
B
C
D
6. Which of the following is a step in solving y = x2 + 5x +6 by the Factoring Method?
A) x + 3 = 0 or x + 2 = 0
B) 2x + 2 = 0 or x + 3 = 0
C) x + 1 = 0 or x + 6 = 0
D) 2x + 6 = 0 or x +1 = 0
7. The solution to (x + 16)2 = 25 is
A) -5 and 5
B) -4 and 4
C) -3 and 3
D) -11 and -21
Algebra II - Quadratics
~13~
NJCTL.org
8. What value goes on the blank to complete the square: x2 - 8x + ___
A) -4
B) -16
C) 16
D) 4
9. What is the discriminant of 2x2 - 8x - 6 = 0
A) -112
B) -16
C) 16
D) 112
10. How many real zeros does an equation have if the discriminant is -9?
A) 0
B) 1
C) 2
D) Not enough information
11. Solve 2x2 - 4x + 6 =0
A.
−4±√−32
B.
C.
D.
4
4±√−32
4
−4±√−48
4
4±√−48
4
12. Simplify
−8±√16
2
A) -6 and -2
B) -4 and -2
C) -4 and -16
D) -6 and -4
13. Given the height of a ball as h = -16t2 + 48t + 32, the class was asked how long was the rock in the air. Kim solved to
find the zeros are t = -.56 and t =3.56, assuming the calculations were correct what should the answer to teacher’s be?
A) -.56 seconds
B) 3.56 seconds
C) 4.12 seconds
D) Not enough information
14. Solve 3x2 + 6x - 9 = 0
A) -3 and -1
B) 3 and 1
C) 3 and -1
D) -3 and 1
15. The vertex of 𝑦 = −3(𝑥 − 4)2 + 8
A) (4,8)
B) (-4,8)
C) (4,-8)
D) (-4,-8)
Algebra II - Quadratics
~14~
NJCTL.org
Extended Response
1. A quadratic’s equation in standard form is 𝑦 = 𝑥 2 − 4𝑥 + 7.
a. What is the vertex form of the quadratic?
b. What is the quadratic’s y-intercept?
c.
Why is the constant different for both forms of the same quadratic?
d. What are the x-intercepts?
e. Which equation did you use from part c and why?
2. The height of Carl, The Human Cannonball, is given by h(t) = −16𝑡 2 + 56𝑡 + 40, in feet t seconds after launch.
a. What was his height at launch?
b. When does he land in the safety net which is 8’ off the ground?
c.
What is his maximum height?
3. The vertex of a parabola is (4,1) and it opens down at twice the rate of the parent function.
a. Write the equation of the parabola in vertex form.
b. Does the parabola have a maximum or a minimum? Where is it? Explain.
c.
What is the y-intercept?
d. What is the x-intercept?
Algebra II - Quadratics
~15~
NJCTL.org
Answers
1. 𝑦 = 3𝑥 2 − 3
2. Not quadratic
42. horizontal shrink of
1
5
1
4
4
2
3. Yes 𝑦 = 𝑥 2 − 𝑥 −
2
43. vertical stretch of 4
4. Yes 4𝑥 2 − 4𝑥 − 2 = 0
5. Not quadratic
6. Up; (0,-4) min; D: reals, R: [-4, infinity); x=0;
2 and -2
7. Down, (1,2) max, D: reals; R: (negative
infinity, 2]; x=1; 0 and 2
8. Not quadratic
9. 𝑦 = −𝑥 2 + 4𝑥 − 6
10. 𝑦 = −4𝑥 2 − 5𝑥 − 1
11. 4𝑥 2 + 6𝑥 − 2 = 0
12. 𝑥 2 − 2𝑥 + 7 = 0
13. Down; (2,8) max; d:reals; R: (negative
infinity, 8]; x=2; 0 and 4
14. Up; (-3,-2) min; D:reals; R:[-2, infinity); x=-3;
-4.5 and -1.5
15. X=-1; (-1, 0); (0,1)
16. X=3; (3, -1); (0,8)
17. X=2; (2, -6); (0,-2)
18. X=-3/2; (-3/2,-3/2); (0,3)
19. X=2/3; (2/3, -10/3); (0, -2)
20. Up; narrower; (0,-4)
21. Down; wider; (0,3)
22. Down; narrower (0,6)
23. Up; narrower; (0.0)
24. Down; narrower (0,0)
25. X=-1; (-1,-9) (0,-8)
26. X=2; (2, -1) (0,3)
27. X=-3; (-3, -12.5); (0,-8)
28. X=-7/2; (-7/2, -25/4) (0,6)
29. X=2/3; (2/3, -4/3) (0,0)
30. Down, wider, (0,-6)
31. Up, narrower, (0,5)
32. Down, narrower (0,8)
33. Up; narrower; (0,0)
34. Up; narrower; (0,0)
35. up 4
36. down 2
37. right 2
38. left 3
39. reflects over x-axis
40. no change, symmetric about y-axis
41. vertical stretch of 3
Algebra II - Quadratics
1
~16~
44. vertical shrink of .3
45. 1 left, reflect over x-axis and vertical stretch
of 2
46. 3 right, up 4
47.
48.
49.
50.
51.
52.
53.
54.
55.
56.
57.
58.
59.
60.
61.
62.
63.
64.
65.
66.
67.
68.
69.
70.
71.
72.
73.
74.
75.
76.
77.
78.
79.
80.
81.
82.
83.
84.
85.
86.
1 and -5
1 and 3
1 and 3
None
-5 and -3
-4
2 and -5
-1
-2/3 and 2
1 and -6
-1 and 3
5 and 1
-2 and 5
-3
-4 and 3
None
-1/2 and -2
-1/3 and 4
(a+3)(a+1)=0; -3 and-1
(b-5)(b+1)=0; 5 and -1
-1(c+7)(c-1)=0; -7 and 1
(d+6)(D+2)=0; -6 and -2
–(e-3)(e+3)=0; 3 and -3
(f+2)(f+2)=0; -2 and -2
-1(g-3)(g-2)=0; 3 and 2
(2h+3)(h+2)=0; -3/2 and -2
(3j-1)(j-1)=0; 1/3 and 1
(a+5)(a+1)=0; -5 and -1
(b-3)(b+2)=0; 3 and -2
(c+4)(c+2)=0; -4 and -2
(d+5)(d+2)=0; -5 and -2
–(e-4)(e+4)=0; 4 and -4
(f+3)(f+3)=0; -3
–(g-6)(g-1)=0; 6 or 1
(2h+2)(h+3)=0; -3 or -1
(3j-4)(j-1)=0; 1 or 4/3
𝑚 = ±4
𝑛 = ±5
𝑝 = ±2
𝑞 = ±4
NJCTL.org
87. 𝑟 = ±3
88. 𝑠 = ±3
89. 𝑡 = ±1
90. 𝑢 = ±2
91. 𝑣 = 7 ± 4 = 11 𝑜𝑟 3
92. w=8 or -2
93. (x-6)2 = 25; 11 or 1
94. m=+/- 6
95. n=+/- 8
96. p=+/- 3
97. q=+/- 2
98. r=+/- 4
99. s=+/- 4
100.
t=+/- 3
101.
u=+/- 1
102.
v=5 or -1
103.
w=0 or -8
104.
2(x+5)2 = 72; 1 or -11
105.
16
106.
25
107.
4
108.
9
109.
12.25
110.
6.25
111.
2 or -8
112.
7 or 1
113.
-1 or -9
114.
13 or -1
115.
−7 ± √29 = -1.61 or -12.39
116.
0 or -8
117.
2 ± 2√6
118.
0.424 and -9.424
119.
5.93 seconds and .07 seconds
120.
36
121.
0.25
122.
49
123.
64
124.
20.25
125.
0.25
126.
2 or -6
127.
9 or 1
128.
−7 ± √34
129.
21 or -1
130.
8 or -10
131.
-6 or 0
132.
3 ± 𝑖√2
133.
1 or -6
134.
.06 sec and 9.94 sec
Algebra II - Quadratics
135.
136.
137.
138.
139.
140.
141.
142.
143.
144.
145.
146.
147.
148.
149.
150.
151.
152.
153.
154.
155.
156.
157.
158.
159.
160.
161.
162.
163.
164.
165.
166.
167.
168.
169.
170.
171.
172.
173.
~17~
7𝑖
−5 − 9𝑖
2+𝑖
32 − 8𝑖
−7 − 6𝑖
−48 − 14𝑖
73
−9−𝑖
2
−44−53𝑖
73
−2+63𝑖
137
−15𝑖
15 + 𝑖
4+𝑖
−30 − 12𝑖
−56 − 8𝑖
55 − 48𝑖
2 − 30𝑖
−4−8𝑖
5
19−40𝑖
53
29−3𝑖
10
−8±2√22
2
4±2√2
= 2 ± √2
2
−4±√13
6
−3±1
= −4 ± √22
=
−2±√13
3
1
= 𝑜𝑟 1
−4
2
5±3√17
8
−7±√193
−18
=
7±√193
18
7 ℎ𝑟𝑠
−7±√69
2
5±√13
2
-3 or 0.5
−2±√19
3
5±√65
10
3±√201
12
9 ℎ𝑟𝑠
16; 2 real roots; 5 and 1
64; 2 real roots; 1 and -3
-71; no real roots
0; 1 real root; 3
-60; no real roots
NJCTL.org
174.
113; 2 real irrational roots;
175.
105; 2 real irrational roots;
9±√113
8
5±√105
4
176.
-16t2+20t+5=30; discriminant = -1200;
no real solution; rock will not reach 30 ft
high.
177.
-3; no real solution
178.
0; 1 real solution; 1
179.
-199; no real solution
180.
1; 2 real solutions; 1.5 and 2
181.
-71; no real solution
182.
145; 2 real irrational solutions;
183.
88; 2 real irrational solutions;
7±√145
6
−6±√22
2
184.
-16t2+64t+5=50; discriminant=1216; 2
real solutions; The vertex is (-2, 69) and the
parabola is open downward so rock reaches
50 feet twice; once on the way up; once on
the way down
185.
(2, 10), up, x=2
186.
(-5,-4), down, x=-5
187.
(6,8), down, x=6
188.
(-7,0), up, x=-7
189.
(3,4), up, x=3
190.
(-2,-5), down, x=-2
191.
(4,6),down, x=4
192.
(0,-4),up, x=0
193.
𝑦 = (𝑥 + 3)2 − 7
194.
𝑦 = (𝑥 − 5)2 − 5
195.
𝑦 = (𝑥 + 4)2 − 28
196.
𝑦 = (𝑥 + 2.5)2 − 3.25
197.
𝑦 = (𝑥 + .5)2 − 1.25
198.
𝑦 = (𝑥 + 2)2
199.
200.
201.
202.
203.
204.
205.
206.
207.
208.
209.
𝑦 = 3(𝑥 + 1)2 − 5
𝑦 = 2(𝑥 − 3)2 − 22
𝑦 = −6(𝑥 − 1)2 + 8
𝑦 = −5(𝑥 + 1)2 + 2
(3.1); down; x=3
(-6,0); up; x=-6
(-4,1): down; x=-4
(8,11); up; x=8
(-2,-3); down; x=-2
(-1,-2); down; x=-1
(3,8); up; x=3
Algebra II - Quadratics
210.
211.
212.
213.
214.
215.
216.
217.
218.
219.
220.
221.
222.
223.
224.
225.
226.
227.
228.
229.
(0,-3); up; x=0
𝑦 = (𝑥 + 4)2 − 14
𝑦 = (𝑥 − 6)2 − 16
𝑦 = (𝑥 + 2)2 − 16
𝑦 = (𝑥 + 1.5)2 + .75
𝑦(𝑥 + 3.5)2 − 13.25
𝑦 = (𝑥 + 3)2
𝑦 = 4(𝑥 + 1.5)2 − 11
𝑦 = −6(𝑥 − 2)2 + 20
𝑦 = 3(𝑥 − 3)2 − 25
𝑦 = −2(𝑥 + 2.5)2 + 9.5
16 and 17
22 and24
15 and 17
239.12 miles
61.35 miles east
S=7ft; P=28ft
X=120; A= 18,000ft2
1/9
(x+2)(2x-1)=88
X=-7.5 or 6
Length = 8 feet
230.
231.
232.
233.
234.
235.
236.
237.
238.
18 and 19
12 and 14
21 and 23
371.31 miles
55.69 miles
P=34 ft
A=2925 ft 2
1/16
(x-4)(2x+3)=76
X=-5.5 or 8
Length= 4 feet
Unit Review Answers:
Multiple Choice:
1. D
2. B
3. B
4. C
5. C
~18~
NJCTL.org
6. A
7. D
8. C
9. D
10. A
11. B
12. A
13. B
14. D
15. A
Extended Response:
1a) 𝑦 = (𝑥 − 2)2 + 3
b) (0,7)
c) The equations are in different forms which
tell you different information about the
quadratic.
d) none
e) answers vary:
standard form – check discriminant which is
negativeno zeros
vertex form – realize vertex is at (2,3) and
parabola is opening upwards no zeros
2a) 40 feet
b) t=4 seconds
c) 89 feet
3a) 𝑦 = −2(𝑥 − 4)2 + 1
b) maximum at (4,1); parabola opens
downward, vertex is maximum
c) (0,-31)
d)
−8±√2
;
2
(3.293,0) and (4.707,0)
Algebra II - Quadratics
~19~
NJCTL.org