Quadratics
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 xintercepts, 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
2
x
x
-9
-8
-7
-6
-5
-4
-3
-2
-1
1
2
3
4
5
6
7
8
-9
9
-8
-7
-6
-5
-4
-3
-2
-1
1
-2
-2
-4
-4
2
3
4
5
6
7
8
9
-6
-6
-8
-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 xintercepts, 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
2
x
-9
-8
-7
-6
-5
-4
-3
-2
-1
1
2
3
4
5
6
7
8
9
x
-9
-8
-7
-6
-5
-4
-3
-2
-1
1
-2
-2
-4
-4
-6
-6
-8
-8
2
3
4
5
6
7
8
9
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 +3x -4
16. y= x2 -5x +6
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 - 3x +2
27. y= x2 - 5x -1
28. y= 2x2 +5x +4
29. y= 3x2 - 2x
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
Graphing to Find Zeros
Class Work
y
8
y
Find the zeros of the following quadratics:
8
35.
6
36.
6
4
4
2
2
x
-9
-8
-7
-6
-5
-4
-3
-2
-1
1
x
-9
-8
-7
-6
-5
-4
-3
-2
-1
1
2
3
4
5
6
7
8
9
-2
-2
-4
-4
-6
-6
-8
-8
2
3
4
5
6
7
8
9
37. y = x2 -4x +3
38. h(x) = -x2 +3x -8
39. y = -x2 -8x -15
40. y = -x2 -8x -16
41. f(x) = x2 +3x -10
42. g(x) = 2x2 +4x +2
43. y = -3x2 +4x +4
Homework
Find the zeros of the following quadratics:
44.
45.
y
y
8
8
6
6
4
4
2
2
x
-9
-8
-7
-6
-5
-4
-3
-2
-1
1
2
3
4
5
6
7
8
x
9
-9
-8
-7
-6
-5
-4
-3
-2
-1
1
-2
-2
-4
-4
-6
-6
-8
-8
46. y = x2 -6x +5
47. y = -x2 +3x +10
48. y = x2 +6x +9
49. f(x) = x2 +x -12
50. y = x2 +2x +4
51. g(x) = 2x2 +5x +2
52. y = -3x2 +11x +4
Solving by Factoring
Class Work
Solve the following quadratics by factoring.
53. a2 +4a +3= 0
54. b2 -4b -5= 0
55. -c2 -6c = -7
56. d2 +8d = -12
57. -e2 +9 = 0
58. f2 +4f +4 = 0
59. –g2 +5g = 6
2
3
4
5
6
7
8
9
60. 2h2 +7h +6= 0
61. 3j2 -4j = -1
62. 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.
Home Work
Solve the following quadratics by factoring.
63. a2 +6a +5= 0
64. b2 -b -6= 0
65. -c2 -6c = 8
66. d2 +7d = -10
67. -e2 +16 = 0
68. f2 +6f +9 = 0
69. –g2 +7g = 6
70. 2h2 +8h +6= 0
71. 3j2 -7j = -4
72. 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.
Solving Using the Square Roots Method
Class Work
Solve the following quadratics using the square roots method
73. m2 = 16
74. n2 = 25
75. 3p2 = 12
76. 5q2 = 80
77. r2 -3 =6
78. s2 +8 =17
79. 2t2 -6 = -4
80. 3u2 +5 = 17
81. (v -7)2 -5 = 11
82. 2(w -3)2 +6 = 56
83. 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
84. m2 = 36
85. n2 = 64
86. 3p2 = 27
87. 5q2 = 20
88. r2 -3 = 13
89. s2 +8 = 24
90. 2t2 -6 = 12
91. 3u2 +5 = 8
92. (v -2)2 +4 = 13
93. 3(w +4)2 -4 = 44
94. 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.
95. a2 + 8a +__
96. b2 + 10b +__
97. c2 - 4c +__
98. d2 - 6d +__
99. e2 + 7e +__
100.
f2 - 5f +__
Solve the following quadratics by completing the square.
101.
h2 + 6h =16
102.
j2 - 8j = -7
103.
k2 + 9 = -10k
104.
m2 - 13 = 12m
105.
14n + 20 = -n2
106.
8p + p2 = 0
107.
2q2 - 8q = 40
108.
3r2 + 27r = 12
109.
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.
110.
a2 + 12a +__
111.
b2 + b +__
112.
c2 - 14c +__
113.
d2 - 16d +__
114.
e2 + 9e +__
115.
f2 - 1f +__
Solve the following quadratics by completing the square.
116.
h2 + 4h =12
117.
j2 - 10j = -9
118.
k2 + 13 = -14k
119.
m2 - 21 = 20m
120.
2n + 80= -n2
121.
6p + p2 = 0
122.
2q2 - 12q = -22
123.
3r2 + 15r = 18
124.
A toy rocket launched into the air has a height (h feet) at any given time (t seconds) as
h = -16t2 + 160t until it hits the ground. At what time(s) is it at a height of 9 feet above the
ground?
Solving Using the Quadratic Formula
Class Work
Solve the following using the quadratic formula. Leave irrational answers in radical form.
125.
x2 +8x -6 =0
126.
g2 -4g +2 =0
127.
3d2 + 4d -3 =0
128.
-2m2 + 3m = 1
129.
4w2 -8 = 5w
130.
7z – 9z2 = -4
131.
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.
132.
x2 +7x -5 =0
133.
g2 -5g +3 =0
134.
2d2 + 5d -3 =0
135.
-3m2 + 4m = -5
136.
5w2 -2 = 5w
137.
3z – 6z2 = -8
138.
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.
139.
x2 - 6x + 5 = 0
140.
2x2 - 4x - 6 = 0
141.
3x + 4x2 + 5 = 0
142.
6x – 9 = x2
143.
3x2 = 6x – 8
144.
4x2 - 9x – 2= 0
145.
x (2x – 5) = 10
146.
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.
147.
3x2 - 9x + 7 = 0
148.
2x2 - 4x + 2 = 0
149.
5x + 7x2 + 8 = 0
150.
7x – 6 = 2x2
151.
5x2 = 7x – 6
152.
3x2 - 7x – 8= 0
153.
(x + 3)(2x + 6) = 11
154.
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.
Mixed Application Problems
Class Work
Solve the following problems using any method.
155.
The product of two consecutive positive integers is 272, find the integers.
156.
The product of two consecutive positive even integers is 528, find the integers.
157.
The product of two consecutive odd integers is 255, find the integers.
158.
Two planes leave airport at the same time (from different runways). 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?
159.
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?
160.
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?
161.
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?
162.
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?
Homework
Solve the following problems using any method.
163.
The product of two consecutive positive integers is 342, find the integers.
164.
The product of two consecutive positive even integers is 168, find the integers.
165.
The product of two consecutive odd integers is 483, find the integers.
166.
Two planes leave airport at the same time (from different runways). 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?
167.
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?
168.
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?
169.
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?
170.
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?
Factoring
Class Work
Factor Completely
171.
2𝑡 2 − 8
172.
6𝑥 − 2 − 9𝑥𝑦 + 3𝑦
173.
𝑟 4 − 16
174.
16𝑥 2 − 121
175.
4𝑐 3 + 24𝑐 2 + 36𝑐
176.
5𝑔2 + 𝑔3 − 5 − 𝑔
177.
3w5z2 – 12w4z2 – 15w3z2
178.
𝑑8 − 1
Homework
Factor Completely
179.
27 – 3x2
180.
5w – 1 – 15wx + 3x
181.
81g4 – 1
182.
32x2 – 50
183.
6e4 + 15e3 + 6e2
184.
5x2 +20x+15
185.
40w5z2 – 200w5z3 + 250w5z4
186.
d4 + 1
Solving Equations by Factoring
Class Work
Solve by Factoring
187.
w2 – w = 0
188.
d2 – 7d + 12 = 0
189.
c2 – 4 = 0
190.
3e2 – 9e + 6 = 0
191.
8t3 – 2t = 0
192.
x2 – 12x = -36
193.
h(h – 1) = 6
194.
b4 – 4b2 = b2 – 4
195.
The height of a toy rocket can be found at any time by the equation h = -16t2 + 80t – 96, at what
time will it hit the ground?
Homework
Solve by Factoring
196.
2c2 – 6c = 0
197.
d2 – 4d – 12 = 0
198.
w2 – 16 = 0
199.
2x2 – 7x + 6 = 0
200.
8a3 – 32a = 0
201.
y2 – 9y = 36
202.
2m2 – 3m = 4m – 5
203.
204.
b6 – b4 = b2 – 1
The length of a rectangle is (x – 2)ft and its width is (x + 3). If its area is 6 sq. ft., find its length.
Solving Rational Equations
Class Work
Find the possible solutions of x. Determine which, if any, work.
205.
206.
207.
208.
209.
210.
211.
212.
213.
2
x+3
4
=
2x−1
2x−1
2
5
2x
2
−
x+3
2
x−3
3
x+2
x
x+5
2
3
x−2
6
=
x+5
x+3
+
=
x
5
+ =
2
+
−
−
x2 −4
6x
=
10
x+3
3
=
x2 −9
4
x−3
1
+
4
1
x+3
4x
x−1
2
5
=
−1
x+3
5
x2 +x−2
1
=
x2 +2x−15
3
=
x−2
x+2
−
5
x2 −4x+4
Homework
Find the possible solutions of x. Determine which, if any, work.
214.
215.
216.
217.
218.
219.
220.
221.
222.
2
x−1
5
=
3x+4
3x+1
3
5
3x
2
−
x−3
3
x−2
7
x+5
x
5
x+4
6
=
+
3x+6
4−x
x+3
x
5
=
+ =
3
+
−
2x+1
2
=
x−1
x2 +4x+3
+
2
1
16
=
x2 −4
2
−
6
3
x−3
2x
x−2
2
5x
=
2
x+2
3
x2 +3x−10
x+2
=
2x2 −x−1
3
1
x+3
=
x+1
−
5
x2 +6x+9
Solving Radical Equations
Class Work
Solve each of the following equations.
223.
√𝑥 = 4
3
224.
√𝑥 + 1 = 3
4
225.
√2x = 2
226.
10 = 2√3 − 2𝑥
1
227.
228.
229.
3 − (2𝑥 − 4)3 = 2
√𝑥 + 2 = √2𝑥
3
3
√4x + 1 − √6x − 9 = 0
230.
(8)2 = (4x)3
1
1
231.
232.
233.
√𝑥 − 1 = √𝑥 + 1
√2𝑥 + 4 = √2𝑥 − 6
The distance between (1,4) and (x,8) is 10, find the possible values of x.
Homework
Solve each of the following equations.
234.
√𝑥 = 7
3
235.
√𝑥 − 1 = 4
4
236.
√2x = 3
237.
12 = 2√6 − 4𝑥
238.
239.
240.
4 − 3(5𝑥 − 2)3 = 10
√4𝑥 + 5 = √2𝑥 − 6
3
3
√5x + 2 − √8x − 7 = 0
241.
242.
243.
244.
(6)2 = (3x)3
√𝑥 − 1 = √2𝑥 − 1
√𝑥 + 3 = √𝑥 + 5
The distance between (-2,3) and (x,9) is 8, find the possible values of x.
1
1
1
Quadratic Inequalities
Class Work
Graph each inequality. Use a compound inequality to state the x-intercept.
245.
𝑦 > 𝑥 2 − 4𝑥 + 3
246.
𝑦 < −2𝑥 2 + 7𝑥 + 4
247.
𝑦 ≥ −3(𝑥 + 2)2
248.
𝑦 ≤ (𝑥 + 4)2 + 2
1
2
Solve each inequality.
249.
0 > 𝑥 2 + 5𝑥 + 6
250.
0 < 𝑥 2 + 𝑥 − 12
251.
0 ≥ −𝑥 2 − 5𝑥
252.
0 ≤ −2𝑥 2 + 6𝑥 + 4
253.
𝑥 2 − 3𝑥 + 2 > 0
254.
−𝑥 2 − 5𝑥 − 12 ≤ 0
255.
𝑥 2 + 4𝑥 ≤ −4
256.
−4𝑥 + 21 > 𝑥 2
Homework
Graph each inequality. Use a compound inequality to state the x-intercept.
257.
𝑦 ≤ 𝑥 2 − 4𝑥 + 4
258.
𝑦 ≥ 2𝑥 2 + 8𝑥 + 6
259.
𝑦 < −4(𝑥 + 3)2
260.
3
𝑦 > (𝑥 − 3)2 + 1
2
Solve each inequality.
261.
0 ≤ 𝑥 2 + 7𝑥 + 10
262.
0 > 𝑥 2 + 4𝑥 − 12
263.
0 < −𝑥 2 + 4𝑥
264.
0 > −3𝑥 2 + 2𝑥 + 8
265.
𝑥 2 + 3𝑥 + 2 > 0
266.
𝑥 2 − 4𝑥 − 12 ≥ 0
267.
𝑥 2 + 8𝑥 ≤ −16
268.
−3𝑥 + 10 > 𝑥 2
Answers
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
11.
12.
13.
14.
15.
16.
17.
18.
19.
20.
21.
22.
23.
24.
25.
26.
27.
28.
Y=3x2-3
NO
Yes y=1/4x2-5/4x-1/2
Yes y=-4x2+4x+2
No
Up; (0,-3) min; D: reals, R: (-3, infinity); x=0;
2 and -2
Down, (1,2) max, D: reals; R: (negative
infinity, 2]; x=1; 0 and 2
No
Y=-x2+4x-6
Y=4x2_5x-1
0=-4x2-6x+2
0=-x2+2x-7
Down; (2,8) max; d:reals; R: (negative
infinity, 8]; x=2; 0 and 4
Up; (-3,-2); D:reals; R:[-2, infinity); x=-3; -4.5
and -1.5
X=-3/2; (-3/2, -6.25); (0,-4)
X=5/2; (5/2, -.25); (0,6)
X=-2; (-2, 10); (0,-2)
X=-3/2; (-3/2,-3/2); (0,3)
X=2/3; (2/3, -10/3)
Up; narrower; (0,-4)
Down; wider; (0,3)
Down; narrower (0,6)
Up; wider; (0.0)
Down; narrower (0,0)
X=-1; (-1,-9) (0,-8)
X=-3/2; (-3/2, -.25) (0,2)
X=5/2; (5/2, -7.25); (0,-1)
X=-5/4; (-5/4, .875) (0,9)
29.
30.
31.
32.
33.
34.
35.
36.
37.
38.
39.
40.
41.
42.
43.
44.
45.
46.
47.
48.
49.
50.
51.
52.
53.
54.
55.
56.
57.
58.
59.
60.
X=1/3; (1/3, -1/3) (0,0)
Down, wider, (0,-6)
Up, narrower, (0,5)
Down, narrower (0,8)
Up; narrower; (0,0)
Up; narrower; (0,0)
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 an d-1
(b-5)(b+1)=0; 5 and 7
-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
-1(g-3)(g-2)=0; 3 and 2
(2h+3)(h+2)=0; -3/2 and -2
61. (3j-1)(j-1)=0; 1/3 and 1
62. (x+2)(2x-1)=88
2x2+3x-2=88
2x2+3x-90=0
(2x+15)(x-6)=0
X=-7.5 or 6
63.
64.
65.
66.
67.
68.
69.
70.
71.
72.
73.
74.
75.
76.
77.
78.
79.
80.
81.
82.
83.
84.
85.
86.
87.
88.
89.
90.
91.
92.
93.
94.
95.
96.
97.
(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 and -3
–(g-6)(g-1)=0; 6 and 1
(2h+2)(h+3)=0
(3j-1)(j-4)=0
(x-4)(2x+3)=76
2x2-5x-88=0
(2x+11)(x-8)=0
X=-5.5 or 8
Length= 4 feet
+/- 4
+/- 5
+/- 2
+/- 4
+/- 3
+/- 3
+/- 1
+/- 2
7+/- 4 = 11 or 3
8 or -2
(x-6)2 = 2i; 11 or 1
+/- 6
+/- 8
+/- 3
+/- 2
+/- 4
+/- 4
+/- 3
+/- 1
5 or 1
0 or -8
2(x+5)2 = 72; -1 or -11
16
25
4
98. 9
99. 12.25
100.
6.15
101.
2 or -8
102.
7 or 1
103.
-1 or -9
104.
13 or -1
105.
-7 +/- √29= -1.61 or -12.39
106.
0 or -8
107.
8 or -4
108.
1.92 or -7.92
109.
5.93 seconds and .07 seconds
110.
36
111.
25
112.
49
113.
64
114.
20.25
115.
25
116.
2 or -6
117.
9 or 1
118.
87 or -14.87
119.
21 or -1
120.
-1 +/- 8.89i
121.
-6 or 0
122.
3 +/- 1.41i
123.
1.99 or -6.99
124.
.06 sec and 9.94 sec
125.
126.
127.
128.
129.
130.
131.
132.
133.
134.
135.
136.
137.
138.
139.
−8±2√11
2
4±2√2
= 2 +/−√2
2
−4±√13
6
−3±1
= −4 +/−√11
=
−2±√13
3
1
= 𝑜𝑟 1
−4
2
5±√153
8
−7±√193
−18
=
7±√193
18
7 ℎ𝑟𝑠
−7±√69
2
5±√13
2
1 or -6
−4±√76
6
5±√65
=
−2±√19
3
10
−3±√201
−12
9 ℎ𝑟𝑠
16; 2 real roots; 5 and 1
140.
141.
142.
143.
64; 2 real roots; 1 and -3
-44; no real roots
0; 1 real root; 3
-60; no real roots
144.
113; 2 real irrational roots;
145.
105; 2 real irrational roots;
9±√113
8
5±√105
4
146.
-16t2+20t+5=30; discriminant = -1200;
no real solution; rock will not reach 30 ft
high.
147.
-3; no real solution
148.
0; 1 real solution; 1
149.
-111; no real solution
150.
1; 2 real solutions; 1.55 and 2
151.
-71; no real solution
152.
145; 2 real irrational solutions;
153.
88; 2 real irrational solutions;
7±√145
6
−12±2√22
4
=
−6±√22
2
154.
-16t2+64t+5=50; discriminant=1216; 2
real solutions; rock reaches 50 feet twice;
once on the way up; once on the way down
155.
16 and 17
156.
22 and24
157.
15 and 17
158.
458 miles
159.
1.3 miles east
160.
S=7ft; f=28ft
161.
X=120; A= 18,000ft2
162.
1/9
163.
18 and 19
164.
12 and 14
165.
21 and 23
166.
371 miles
167.
71 miles
168.
P=34 ft
169.
A=2925 ft 2
170.
16/1
171.
2(t-4)(t+4)
172.
(3x-1)(2-3y)
173.
(r2+4)(r-2)(r+2)
174.
(4x-11)(4x+11)
175.
4c(c+3)(c+3)
176.
(5+g)(g-1)(g+1)
177.
3w3z2(w-5)(w+1)
178.
(d4+1)(d2+1)(d-1)(d+1)
179.
3(3-x)(3+x)
180.
(5w-1)(1-3x)
181.
182.
183.
184.
185.
186.
187.
188.
189.
190.
(9g2+1)(3g-1)(3g+1)
2(4x-5)(4x+5)
3e2(2e+1)(e+2)
5(x+3)(x+1)
10w5z2(2-5z)(2-5z)
not factorable
{0,1}
{3,4}
{±2}
{1,2}
191.
{0,± }
1
2
192.
{6}
193.
{-2, 3}
194.
{±1, ±2}
195.
Clears the ground in 2 seconds, lands in
3 seconds (rocket was launched 96 ft below
ground level)
196.
{0, 3}
197.
{-2, 6}
198.
{±4}
199.
{1, 3}
200.
{0, ±2}
201.
{-3, 12}
5
202.
{1, }
203.
204.
{±1}
2 ft
205.
-13
13/4
-2
6/7
-17/5
-3/7
16
206.
207.
208.
209.
210.
211.
212.
213.
214.
215.
216.
217.
218.
219.
220.
2
5+/−√69
2
19+/−√281
4
13/3
2
7
-8/15
12/5
38/11
27/5
221.
222.
223.
224.
225.
226.
227.
228.
229.
230.
231.
232.
233.
234.
235.
236.
237.
238.
239.
240.
241.
242.
243.
244.
245.
6
No real solution
252.
−.562 ≤ 𝑥 ≤ 3.562
253.
𝑥 < 1 𝑜𝑟 𝑥 > 2
16
26
8
-11
2.5
2
5
4√2
No solution
No solution
1 +/- 2√21
49
65
40.5
-7.5
-6/5
No solution
3
2√6
2
No solution
-2 +/- 2√7
254.
all reals
255.
x=-2
256.
−7 < 𝑥 < 3
257.
solid
1<𝑥<3
Dotted
Boundary
−1
<𝑥<4
2
247.
Solid
Bounds
𝑥 = −2
248.
𝑎𝑙𝑙 𝑟𝑒𝑎𝑙𝑠
258.
Solid
all reals
249.
−3 < 𝑥 < −2
250.
𝑥 < −4 𝑜𝑟 𝑥 > 3
251.
𝑥 ≤ −5 𝑜𝑟 𝑥 ≥ 0
solid
boundary
−3 ≤ 𝑥 ≤ −1
259.
dotted
boundary
no solution
260.
dotted boundary
no solution
261.
𝑥 ≤ −5 𝑜𝑟 𝑥 ≥ −2
262.
−6 < 𝑥 < 2
263.
0<𝑥<4
264.
Dotted
Boundary
246.
boundary
−4
3
<𝑥<2
265.
𝑥 < −2 𝑜𝑟 𝑥 > −1
266.
𝑥 < −2 𝑜𝑟 𝑥 > 6
267.
𝑥 = −4
268.
−5 < 𝑥 < 2