4 Characteristics of Quadratics -9 -8 -7 -6 -5 -4 -3 -2 -1...

Algebra II - Quadratics ~1~ NJCTL.org

-9 -8 -7 -6 -5 -4 -3 -2 -1 1 2 3 4 5 6 7 8 9

-8

-6

-4

-2

2

4

6

8

x

y

-9 -8 -7 -6 -5 -4 -3 -2 -1 1 2 3 4 5 6 7 8 9

-8

-6

-4

-2

2

4

6

8

x

y

-9 -8 -7 -6 -5 -4 -3 -2 -1 1 2 3 4 5 6 7 8 9

-8

-6

-4

-2

2

4

6

8

x

y

-9 -8 -7 -6 -5 -4 -3 -2 -1 1 2 3 4 5 6 7 8 9

-8

-6

-4

-2

2

4

6

8

x

y

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

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


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. f(x) = 2x2 +3x -4

21. y = -.7x2 -4x +3

22. y = -1.2x2 +6

23. g(x) = 3x2 +3x

24. 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. f(x) =-.6x2 +3x -6

31. y = 1.7x2 -4x +5

32. y = -1.02x2 +8

33. g(x) = 1.3x2 +4x

34. y = 5x2


-9 -8 -7 -6 -5 -4 -3 -2 -1 1 2 3 4 5 6 7 8 9

-8

-6

-4

-2

2

4

6

8

x

y

-9 -8 -7 -6 -5 -4 -3 -2 -1 1 2 3 4 5 6 7 8 9

-8

-6

-4

-2

2

4

6

8

x

y

Transformations

Class Work

In each exercise the function is given. Describe the transformation of the parent function. Graph the function.

35. 𝑓(𝑥) = 𝑥2 + 4

36. 𝑔(𝑥) = 𝑥2 − 2

37. 𝑓(𝑥) = (𝑥 − 2)2

38. 𝑔(𝑥) = (𝑥 + 3)2

39. 𝑓(𝑥) = −𝑥2

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) = 3𝑥2

42. 𝑔(𝑥) = (2𝑥)2

43. 𝑓(𝑥) = (1

2𝑥)

2

44. 𝑔(𝑥) = . 3𝑥2

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.

48.


-9 -8 -7 -6 -5 -4 -3 -2 -1 1 2 3 4 5 6 7 8 9

-8

-6

-4

-2

2

4

6

8

x

y

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.

-9 -8 -7 -6 -5 -4 -3 -2 -1 1 2 3 4 5 6 7 8 9

-8

-6

-4

-2

2

4

6

8

x

y

57.

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


Solving by Factoring

Class Work

Solve the following quadratics by factoring.

65. a2 +4a +3= 0

66. b2 -4b -5= 0

67. -c2 -6c = -7

68. d2 +8d = -12

69. -e2 +9 = 0

70. f2 +4f +4 = 0

71. –g2 +5g = 6

72. 2h2 +7h +6= 0

73. 3j2 -4j = -1

Home Work

Solve the following quadratics by factoring.

74. a2 +6a +5= 0

75. b2 -b -6= 0

76. -c2 -6c = 8

77. d2 +7d = -10

78. -e2 +16 = 0

79. f2 +6f +9 = 0

80. –g2 +7g = 6

81. 2h2 +8h +6= 0

82. 3j2 -7j = -4

Solving Using the Square Roots Method

Class Work Solve the following quadratics using the square roots method.

83. m2 = 16

84. n2 = 25

85. 3p2 = 12

86. 5q2 = 80

87. r2 -3 =6


88. s2 +8 =17

89. 2t2 -6 = -4

90. 3u2 +5 = 17

91. (v -7)2 -5 = 11

92. 2(w -3)2 +6 = 56

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

95. n2 = 64

96. 3p2 = 27

97. 5q2 = 20

98. r2 -3 = 13

99. s2 +8 = 24

100. 2t2 -6 = 12

101. 3u2 +5 = 8

102. (v -2)2 +4 = 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 +__


110. f2 - 5f +__

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. 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?

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)


139. (−2 − 𝑖)(4 + 𝑖)

140. (1 − 7𝑖)2

141. (8 − 3𝑖)(8 + 3𝑖)

142. 1−9𝑖

2𝑖

143. 4−7𝑖

3+8𝑖

144. 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. 8−4𝑖

5𝑖

153. 1−6𝑖

7−2𝑖

154. 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


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


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 = −6

5(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 =7

−11(𝑥 − 4)2 + 6

192. 𝑦 = 4(𝑥)2 − 4

Convert the following equations from standard form to vertex form.

193. 𝑦 = 𝑥2 + 6𝑥 + 2

194. 𝑦 = 𝑥2 − 10𝑥 + 20


195. 𝑦 = 𝑥2 + 8𝑥 − 12

196. 𝑦 = 𝑥2 + 5𝑥 + 3

197. 𝑦 = 𝑥2 + 𝑥 − 1

198. 𝑦 = 𝑥2 + 4𝑥 + 4

199. 𝑦 = 3𝑥2 + 6𝑥 − 2

200. 𝑦 = 2𝑥2 − 12𝑥 − 4

201. 𝑦 = −6𝑥2 + 12𝑥 + 2

202. 𝑦 = −5𝑥2 − 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 = −7

2(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

Convert the following equations from standard form to vertex form.

211. 𝑦 = 𝑥2 + 8𝑥 + 2

212. 𝑦 = 𝑥2 − 12𝑥 + 20

213. 𝑦 = 𝑥2 + 4𝑥 − 12

214. 𝑦 = 𝑥2 + 3𝑥 + 3

215. 𝑦 = 𝑥2 + 7𝑥 − 1

216. 𝑦 = 𝑥2 + 6𝑥 + 9

217. 𝑦 = 4𝑥2 + 12𝑥 − 2

218. 𝑦 = −6𝑥2 + 24𝑥 − 4

219. 𝑦 = 3𝑥2 − 18𝑥 + 2

220. 𝑦 = −2𝑥2 − 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.


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?


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


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

4

B. 4±√−32

4

C. −4±√−48

4

D. 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)


Extended Response

1. A quadratic’s equation in standard form is 𝑦 = 𝑥2 − 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) = −16𝑡2 + 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?


Answers

1. 𝑦 = 3𝑥2 − 3

2. Not quadratic

3. Yes 𝑦 =1

4𝑥2 −

5

4𝑥 −

1

2

4. Yes 4𝑥2 − 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 = −𝑥2 + 4𝑥 − 6

10. 𝑦 = −4𝑥2 − 5𝑥 − 1

11. 4𝑥2 + 6𝑥 − 2 = 0

12. 𝑥2 − 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

42. horizontal shrink of 1

2

43. vertical stretch of 4

44. vertical shrink of .3

45. 1 left, reflect over x-axis and vertical stretch

of 2

46. 3 right, up 4

47. 1 and -5

48. 1 and 3

49. 1 and 3

50. None

51. -5 and -3

52. -4

53. 2 and -5

54. -1

55. -2/3 and 2

56. 1 and -6

57. -1 and 3

58. 5 and 1

59. -2 and 5

60. -3

61. -4 and 3

62. None

63. -1/2 and -2

64. -1/3 and 4

65. (a+3)(a+1)=0; -3 and-1

66. (b-5)(b+1)=0; 5 and -1

67. -1(c+7)(c-1)=0; -7 and 1

68. (d+6)(D+2)=0; -6 and -2

69. –(e-3)(e+3)=0; 3 and -3

70. (f+2)(f+2)=0; -2 and -2

71. -1(g-3)(g-2)=0; 3 and 2

72. (2h+3)(h+2)=0; -3/2 and -2

73. (3j-1)(j-1)=0; 1/3 and 1

74. (a+5)(a+1)=0; -5 and -1

75. (b-3)(b+2)=0; 3 and -2

76. (c+4)(c+2)=0; -4 and -2

77. (d+5)(d+2)=0; -5 and -2

78. –(e-4)(e+4)=0; 4 and -4

79. (f+3)(f+3)=0; -3

80. –(g-6)(g-1)=0; 6 or 1

81. (2h+2)(h+3)=0; -3 or -1

82. (3j-4)(j-1)=0; 1 or 4/3

83. 𝑚 = ±4

84. 𝑛 = ±5

85. 𝑝 = ±2

86. 𝑞 = ±4


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

135. 7𝑖

136. −5 − 9𝑖

137. 2 + 𝑖

138. 32 − 8𝑖

139. −7 − 6𝑖

140. −48 − 14𝑖

141. 73

142. −9−𝑖

2

143. −44−53𝑖

73

144. −2+63𝑖

137

145. −15𝑖

146. 15 + 𝑖

147. 4 + 𝑖

148. −30 − 12𝑖

149. −56 − 8𝑖

150. 55 − 48𝑖

151. 2 − 30𝑖

152. −4−8𝑖

5

153. 19−40𝑖

53

154. 29−3𝑖

10

155. −8±2√22

2= −4 ± √22

156. 4±2√2

2= 2 ± √2

157. −4±√13

6=

−2±√13

3

158. −3±1

−4=

1

2𝑜𝑟 1

159. 5±3√17

8

160. −7±√193

−18=

7±√193

18

161. 7 ℎ𝑟𝑠

162. −7±√69

2

163. 5±√13

2

164. -3 or 0.5

165. −2±√19

3

166. 5±√65

10

167. 3±√201

12

168. 9 ℎ𝑟𝑠

169. 16; 2 real roots; 5 and 1

170. 64; 2 real roots; 1 and -3

171. -71; no real roots

172. 0; 1 real root; 3

173. -60; no real roots


174. 113; 2 real irrational roots; 9±√113

8

175. 105; 2 real irrational roots; 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


180. 1; 2 real solutions; 1.5 and 2


182. 145; 2 real irrational solutions; 7±√145

6

183. 88; 2 real irrational solutions; −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. 𝑦 = 3(𝑥 + 1)2 − 5

200. 𝑦 = 2(𝑥 − 3)2 − 22

201. 𝑦 = −6(𝑥 − 1)2 + 8

202. 𝑦 = −5(𝑥 + 1)2 + 2

203. (3.1); down; x=3

204. (-6,0); up; x=-6

205. (-4,1): down; x=-4

206. (8,11); up; x=8

207. (-2,-3); down; x=-2

208. (-1,-2); down; x=-1

209. (3,8); up; x=3

210. (0,-3); up; x=0

211. 𝑦 = (𝑥 + 4)2 − 14

212. 𝑦 = (𝑥 − 6)2 − 16

213. 𝑦 = (𝑥 + 2)2 − 16

214. 𝑦 = (𝑥 + 1.5)2 + .75

215. 𝑦(𝑥 + 3.5)2 − 13.25

216. 𝑦 = (𝑥 + 3)2

217. 𝑦 = 4(𝑥 + 1.5)2 − 11

218. 𝑦 = −6(𝑥 − 2)2 + 20

219. 𝑦 = 3(𝑥 − 3)2 − 25

220. 𝑦 = −2(𝑥 + 2.5)2 + 9.5

221. 16 and 17

222. 22 and24

223. 15 and 17

224. 239.12 miles

225. 61.35 miles east

226. S=7ft; P=28ft

227. X=120; A= 18,000ft2

228. 1/9

229. (x+2)(2x-1)=88

X=-7.5 or 6

Length = 8 feet

230. 18 and 19

231. 12 and 14

232. 21 and 23

233. 371.31 miles

234. 55.69 miles

235. P=34 ft

236. A=2925 ft 2

237. 1/16

238. (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


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 negativeno 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)

Date post:	14-May-2018
Category:	Documents
Upload:	danghuong
View:	213 times
Download:	1 times

4 Characteristics of Quadratics -9 -8 -7 -6 -5 -4 -3 -2 -1...

Documents