 Intermediate Algebra 2e

# Chapter 9

### Be Prepared

9.1

$8282$

9.2

$41054105$

9.3

$3x−223x−22$

9.4

$x2+18x+81x2+18x+81$

9.5

$y−72y−72$

9.6

$5n+425n+42$

9.7

$2828$

9.8

$6363$

9.9

$5252$

9.10

$y2+4y2−5y2+4y2−5$

9.11

$(y−1)(y+1)(y−1)(y+1)$

9.12

$x34x34$; $x23x23$; $x−2x−2$

9.13

$−51,−49−51,−49$

9.14

$x=23x=23$

9.15

$13inches13inches$

9.16 9.17

$x=12,x=−2x=12,x=−2$

9.18

$11$

9.19 9.20

$y−72y−72$

9.21

$2(x−4)22(x−4)2$

9.22

$x=32x=32$

9.23

$y=−3,y=52y=−3,y=52$

9.24

$−∞,−4∪2,∞−∞,−4∪2,∞$

### Try It

9.1

$x=43,x=−43x=43,x=−43$

9.2

$y=33,y=−33y=33,y=−33$

9.3

$x=7,x=−7x=7,x=−7$

9.4

$m=4,m=−4m=4,m=−4$

9.5

$c=23i,c=−23ic=23i,c=−23i$

9.6

$c=26i,c=−26ic=26i,c=−26i$

9.7

$x=210,x=−210x=210,x=−210$

9.8

$y=27,y=−27y=27,y=−27$

9.9

$r=655,r=−655r=655,r=−655$

9.10

$t=833,t=−833t=833,t=−833$

9.11

$a=3+32,a=3−32a=3+32,a=3−32$

9.12

$b=−2+210,b=−2−210b=−2+210,b=−2−210$

9.13

$x=12+52x=12+52$,$x=12−52x=12−52$

9.14

$y=−34+74,y=−34−74y=−34+74,y=−34−74$

9.15

$a=5+25,a=5−25a=5+25,a=5−25$

9.16

$b=−3+42,b=−3−42b=−3+42,b=−3−42$

9.17

$r=−43+22i3,r=−43−22i3r=−43+22i3,r=−43−22i3$

9.18

$t=4+10i2,t=4−10i2t=4+10i2,t=4−10i2$

9.19

$m=73,m=−1m=73,m=−1$

9.20

$n=−34,n=−74n=−34,n=−74$

9.21

$(a−10)2(a−10)2$ $(b−52)2(b−52)2$
$(p+18)2(p+18)2$

9.22

$(b−2)2(b−2)2$ $(n+132)2(n+132)2$
$(q−13)2(q−13)2$

9.23

$x=−5,x=−1x=−5,x=−1$

9.24

$y=1,y=9y=1,y=9$

9.25

$y=5±10iy=5±10i$

9.26

$z=−4+3i,z=−4−3iz=−4+3i,z=−4−3i$

9.27

$x=8+43,x=8−43x=8+43,x=8−43$

9.28

$y=−4+33,y=−4−33y=−4+33,y=−4−33$

9.29

$a=−7,a=3a=−7,a=3$

9.30

$b=−10,b=2b=−10,b=2$

9.31

$p=52+612,p=52−612p=52+612,p=52−612$

9.32

$q=72+372,q=72−372q=72+372,q=72−372$

9.33

$c=−9,c=3c=−9,c=3$

9.34

$d=11,d=−7d=11,d=−7$

9.35

$m=−7,m=−1m=−7,m=−1$

9.36

$n=−2,n=8n=−2,n=8$

9.37

$r=−73,r=3r=−73,r=3$

9.38

$t=−52,t=2t=−52,t=2$

9.39

$x=−38+418,x=−38−418x=−38+418,x=−38−418$

9.40

$y=53+103,y=53−103y=53+103,y=53−103$

9.41

$y=1,y=23y=1,y=23$

9.42

$z=1,z=−32z=1,z=−32$

9.43

$a=−3,a=5a=−3,a=5$

9.44

$b=−6,b=−4b=−6,b=−4$

9.45

$m=−6+153,m=−6−153m=−6+153,m=−6−153$

9.46

$n=−2+265,n=−2−265n=−2+265,n=−2−265$

9.47

$a=14+314i,a=14−314ia=14+314i,a=14−314i$

9.48

$b=−15+195i,b=−15−195ib=−15+195i,b=−15−195i$

9.49

$x=−1+6,x=−1−6x=−1+6,x=−1−6$

9.50

$y=1+2,y=1−2y=1+2,y=1−2$

9.51

$c=2+73,c=2−73c=2+73,c=2−73$

9.52

$d=9+334,d=9−334d=9+334,d=9−334$

9.53

$r=−5r=−5$

9.54

$t=45t=45$

9.55

2 complex solutions; 2 real solutions; 1 real solution

9.56

2 real solutions; 2 complex solutions; 1 real solution

9.57

factoring; Square Root Property; Quadratic Formula

9.58

Factoring or Square Root Property Square Root Property

9.59

$x=2,x=−2,x=2,x=−2x=2,x=−2,x=2,x=−2$

9.60

$x=7,x=−7,x=2,x=−2x=7,x=−7,x=2,x=−2$

9.61

$x=3,x=1x=3,x=1$

9.62

$y=−1,y=1y=−1,y=1$

9.63

$x=9,x=16x=9,x=16$

9.64

$x=4,x=16x=4,x=16$

9.65

$x=−8,x=343x=−8,x=343$

9.66

$x=81,x=625x=81,x=625$

9.67

$x=43x=2x=43x=2$

9.68

$x=25,x=34x=25,x=34$

9.69

The two consecutive odd integers whose product is 99 are 9, 11, and −9, −11

9.70

The two consecutive even integers whose product is 128 are 12, 14 and −12, −14.

9.71

The height of the triangle is 12 inches and the base is 76 inches.

9.72

The height of the triangle is 11 feet and the base is 20 feet.

9.73

The length of the garden is approximately 18 feet and the width 11 feet.

9.74

The length of the tablecloth is approximatel 11.8 feet and the width 6.8 feet.

9.75

The length of the flag pole’s shadow is approximately 6.3 feet and the height of the flag pole is 18.9 feet.

9.76

The distance between the opposite corners is approximately 7.2 feet.

9.77

The arrow will reach 180 feet on its way up after 3 seconds and again on its way down after approximately 3.8 seconds.

9.78

The ball will reach 48 feet on its way up after approximately .6 second and again on its way down after approximately 5.4 seconds.

9.79

The speed of the jet stream was 100 mph.

9.80

The speed of the jet stream was 50 mph.

9.81

Press #1 would take 12 hours, and Press #2 would take 6 hours to do the job alone.

9.82

The red hose take 6 hours and the green hose take 3 hours alone.

9.83 9.84 9.85

up; down

9.86

down; up

9.87

$x=2;x=2;$ $(2, −7)(2, −7)$

9.88

$x=1;x=1;$ $(1, −5)(1, −5)$

9.89

y-intercept: $(0, −8)(0, −8)$ x-intercepts $(−4,0),(2,0)(−4,0),(2,0)$

9.90

y-intercept: $(0, −12)(0, −12)$ x-intercepts $(−2,0),(6,0)(−2,0),(6,0)$

9.91

y-intercept: $(0, 4)(0, 4)$ no x-intercept

9.92

y-intercept: $(0, −5)(0, −5)$ x-intercepts $(−1, 0),(5, 0)(−1, 0),(5, 0)$

9.93 9.94 9.95 9.96 9.97 9.98 9.99 9.100 9.101

The minimum value of the quadratic function is −4 and it occurs when x = 4.

9.102

The maximum value of the quadratic function is 5 and it occurs when x = 2.

9.103

It will take 4 seconds for the stone to reach its maximum height of 288 feet.

9.104

It will 6.5 seconds for the rocket to reach its maximum height of 676 feet.

9.105 The graph of $g(x)=x2+1g(x)=x2+1$ is the same as the graph of $f(x)=x2f(x)=x2$ but shifted up 1 unit. The graph of $h(x)=x2−1h(x)=x2−1$ is the same as the graph of $f(x)=x2f(x)=x2$ but shifted down 1 unit.

9.106 The graph of $h(x)=x2+6h(x)=x2+6$ is the same as the graph of $f(x)=x2f(x)=x2$ but shifted up 6 units. The graph of $h(x)=x2−6h(x)=x2−6$ is the same as the graph of $f(x)=x2f(x)=x2$ but shifted down 6 units.

9.107 9.108 9.109 The graph of $g(x)=(x+2)2g(x)=(x+2)2$ is the same as the graph of $f(x)=x2f(x)=x2$ but shifted left 2 units. The graph of $h(x)=(x−2)2h(x)=(x−2)2$ is the same as the graph of $f(x)=x2f(x)=x2$ but shift right 2 units.

9.110 The graph of $g(x)=(x+5)2g(x)=(x+5)2$ is the same as the graph of $f(x)=x2f(x)=x2$ but shifted left 5 units. The graph of $h(x)=(x−5)2h(x)=(x−5)2$ is the same as the graph of $f(x)=x2f(x)=x2$ but shifted right 5 units.

9.111 9.112 9.113 9.114 9.115 9.116 9.117

$f(x)=−4(x+1)2+5f(x)=−4(x+1)2+5$

9.118

$f(x)=2(x−2)2−5f(x)=2(x−2)2−5$

9.119 9.120 9.121 9.122 9.123

$f(x)=3(x−1)2+2f(x)=3(x−1)2+2$ 9.124

$f(x)=−2(x−2)2+1f(x)=−2(x−2)2+1$ 9.125

$f(x)=(x−3)2−4f(x)=(x−3)2−4$

9.126

$f(x)=(x+3)2−1f(x)=(x+3)2−1$

9.127 $(−4,2)(−4,2)$

9.128 $(−∞,2]∪[6,∞)(−∞,2]∪[6,∞)$

9.129 $(−5,−1)(−5,−1)$

9.130 $(−∞,2]∪[8,∞)(−∞,2]∪[8,∞)$

9.131

$(−∞,−4]∪[2,∞)(−∞,−4]∪[2,∞)$

9.132

$[−3,5][−3,5]$

9.133

$[−1−2,−1+2][−1−2,−1+2]$

9.134

$(−∞,4−2)∪(4+2,∞)(−∞,4−2)∪(4+2,∞)$

9.135

$(−∞,∞)(−∞,∞)$
no solution

9.136

no solution
$(−∞,∞)(−∞,∞)$

### Section 9.1 Exercises

1.

$a=±7a=±7$

3.

$r=±26r=±26$

5.

$u=±103u=±103$

7.

$m=±3m=±3$

9.

$x=±6x=±6$

11.

$x=±5ix=±5i$

13.

$x=±37ix=±37i$

15.

$x=±9x=±9$

17.

$a=±25a=±25$

19.

$p=±477p=±477$

21.

$y=±4105y=±4105$

23.

$u=14,u=−2u=14,u=−2$

25.

$m=6±25m=6±25$

27.

$r=12±32r=12±32$

29.

$y=−23±229y=−23±229$

31.

$a=7±52a=7±52$

33.

$x=−3±22x=−3±22$

35.

$c=−15±335ic=−15±335i$

37.

$x=34±72ix=34±72i$

39.

$m=2±22m=2±22$

41.

$x=3±23x=3±23$

43.

$x=−35,x=95x=−35,x=95$

45.

$x=−76,x=116x=−76,x=116$

47.

$r=±4r=±4$

49.

$a=4±27a=4±27$

51.

$w=1,w=53w=1,w=53$

53.

$a=±32a=±32$

55.

$p=13±73p=13±73$

57.

$m=±23im=±23i$

59.

$u=7±62u=7±62$

61.

$m=4±23m=4±23$

63.

$x=−3,x=−7x=−3,x=−7$

65.

$c=±566c=±566$

67.

$x=6±2ix=6±2i$

69.

### Section 9.2 Exercises

71.

$(m−12)2(m−12)2$ $(x−112)2(x−112)2$
$(p−16)2(p−16)2$

73.

$(p−11)2(p−11)2$ $(y+52)2(y+52)2$
$(m+15)2(m+15)2$

75.

$u=−3,u=1u=−3,u=1$

77.

$x=−1,x=21x=−1,x=21$

79.

$m=−2±210im=−2±210i$

81.

$r=−3±2ir=−3±2i$

83.

$a=5±25a=5±25$

85.

$x=−52±332x=−52±332$

87.

$u=1,u=13u=1,u=13$

89.

$r=−2,r=6r=−2,r=6$

91.

$v=92±892v=92±892$

93.

$x=5±30x=5±30$

95.

$x=−7,x=3x=−7,x=3$

97.

$x=−5,x=−1x=−5,x=−1$

99.

$m=−11,m=1m=−11,m=1$

101.

$n=−1±14n=−1±14$

103.

$c=−2,c=32c=−2,c=32$

105.

$x=−5,x=32x=−5,x=32$

107.

$p=−74±1614p=−74±1614$

109.

$x=310±19110ix=310±19110i$

111.

### Section 9.3 Exercises

113.

$m=−1,m=34m=−1,m=34$

115.

$p=12,p=3p=12,p=3$

117.

$p=−4,p=−3p=−4,p=−3$

119.

$r=−3,r=11r=−3,r=11$

121.

$u=−7±736u=−7±736$

123.

$a=3±32a=3±32$

125.

$x=−4±25x=−4±25$

127.

$y=−2,y=13y=−2,y=13$

129.

$x=−34±154ix=−34±154i$

131.

$x=38±78ix=38±78i$

133.

$v=2±13v=2±13$

135.

$y=3±1932y=3±1932$

137.

$m=−1,m=34m=−1,m=34$

139.

$b=−2±226b=−2±226$

141.

$c=−34c=−34$

143.

$q=−35q=−35$

145.

$no real solutionsno real solutions$ $11$
$22$

147.

$11$ $no real solutionsno real solutions$
$22$

149.

$factorfactor$
$square rootsquare root$
$Quadratic FormulaQuadratic Formula$

151.

$Quadratic FormulaQuadratic Formula$
$square rootsquare root$
$factorfactor$

153.

### Section 9.4 Exercises

155.

$x=±3,x=±2x=±3,x=±2$

157.

$x=±15,x=±2ix=±15,x=±2i$

159.

$x=±1,x=±62x=±1,x=±62$

161.

$x=±3,x=±22x=±3,x=±22$

163.

$x=−1,x=12x=−1,x=12$

165.

$x=−53,x=0x=−53,x=0$

167.

$x=0,x=±3x=0,x=±3$

169.

$x=±222,x=±7x=±222,x=±7$

171.

$x=25x=25$

173.

$x=4x=4$

175.

$x=14x=14$

177.

$x=125, x=94 x=125,x=94$

179.

$x=−1,x=−512x=−1,x=−512$

181.

$x=8,x=−216x=8,x=−216$

183.

$x=278,x=−6427x=278,x=−6427$

185.

$x=27512,x=125x=27512,x=125$

187.

$x=1,x=49x=1,x=49$

189.

$x=−2,x=−35x=−2,x=−35$

191.

$x=−2,x=43x=−2,x=43$

193.

### Section 9.5 Exercises

195.

Two consecutive odd numbers whose product is 255 are 15 and 17, and −15 and −17.

197.

The first and second consecutive odd numbers are 24 and 26, and −26 and −24.

199.

Two consecutive odd numbers whose product is 483 are 21 and 23, and −21 and −23.

201.

The width of the triangle is 5 inches and the height is 18 inches.

203.

The base is 24 feet and the height of the triangle is 10 feet.

205.

The length of the driveway is 15.0 feet and the width is 3.3 feet.

207.

The length of table is 8 feet and the width is 3 feet.

209.

The lengths of the three sides of the triangle are 1.7, 3, and 3.5 ft.

211.

The length of the diagonal fencing is 7.3 yards.

213.

The ladder will reach 24.5 feet on the side of the house.

215.

The rocket will reach 1200 feet on its way up at 1.97 seconds and on its way down at 38.03 seconds.

217.

The bullet will take 70 seconds to hit the ground.

219.

The speed of the wind was 49 mph.

221.

The speed of the current was 4.3 mph.

223.

The less experienced painter takes 6 hours and the experienced painter takes 3 hours to do the job alone.

225.

Machine #1 takes 3.6 hours and Machine #2 takes 4.6 hours to do the job alone.

227.

### Section 9.6 Exercises

229. 231. 233.

down up

235.

down up

237.

$x=−4x=−4$; $(−4, −17)(−4, −17)$

239.

$x=1x=1$; $(1,6)(1,6)$

241.

y-intercept: $(0, 6);(0, 6);$ x-intercept $(−1, 0),(−6, 0)(−1, 0),(−6, 0)$

243.

y-intercept: $(0, 12);(0, 12);$ x-intercept $(−2, 0),(−6, 0)(−2, 0),(−6, 0)$

245.

y-intercept: $(0, −19);(0, −19);$ x-intercept: none

247.

y-intercept: $(0, 13);(0, 13);$ x-intercept: none

249.

y-intercept: $(0,25);(0,25);$ x-intercept $(52,0)(52,0)$

251.

y-intercept: $(0,−9);(0,−9);$ x-intercept $(−3, 0)(−3, 0)$

253. 255. 257. 259. 261. 263. 265. 267. 269. 271.

The minimum value is $−98−98$ when $x=−14.x=−14.$

273.

The minimum value is 6 when x = 3.

275.

The maximum value is 16 when x = 0.

277.

In 5.3 sec the arrow will reach maximum height of 486 ft.

279.

In 3.4 seconds the ball will reach its maximum height of 185.6 feet.

281.

A selling price of $20 per computer will give the maximum revenue of$400.

283.

A selling price of $35 per pair of boots will give a maximum revenue of$1,225.

285.

The length of one side along the river is 120 feet and the maximum are is 7,200 square feet.

287.

The maximum area of the patio is 800 feet.

289.

291.

### Section 9.7 Exercises

293. The graph of $g(x)=x2+4g(x)=x2+4$ is the same as the graph of $f(x)=x2f(x)=x2$ but shifted up 4 units. The graph of $h(x)=x2−4h(x)=x2−4$ is the same as the graph of $f(x)=x2f(x)=x2$ but shift down 4 units.

295. 297. 299. 301. The graph of $g(x)=(x−3)2g(x)=(x−3)2$ is the same as the graph of $f(x)=x2f(x)=x2$ but shifted right 3 units. The graph of $h(x)=(x+3)2h(x)=(x+3)2$ is the same as the graph of $f(x)=x2f(x)=x2$ but shifted left 3 units.

303. 305. 307. 309. 311. 313. 315. 317. 319. 321. 323. 325.

$f(x)=−3(x+2)2+7f(x)=−3(x+2)2+7$

327.

$f(x)=3(x+1)2−4f(x)=3(x+1)2−4$

329.

$f(x)=(x+3)2−4f(x)=(x+3)2−4$ 331.

$f(x)=(x+2)2−1f(x)=(x+2)2−1$ 333.

$f(x)=(x−3)2+6f(x)=(x−3)2+6$ 335.

$f(x)=−(x−4)2+0f(x)=−(x−4)2+0$ 337.

$f(x)=−(x+2)2+6f(x)=−(x+2)2+6$ 339.

$f(x)=5(x−1)2+3f(x)=5(x−1)2+3$ 341.

$f(x)=2(x−1)2−1f(x)=2(x−1)2−1$ 343.

$f(x)=−2(x−2)2−2f(x)=−2(x−2)2−2$ 345.

$f(x)=2(x+1)2+4f(x)=2(x+1)2+4$ 347.

$f(x)=−(x−1)2−3f(x)=−(x−1)2−3$ 349.

351.

353.

355.

357.

$f(x)=(x+1)2−5f(x)=(x+1)2−5$

359.

$f(x)=2(x−1)2−3f(x)=2(x−1)2−3$

361.

### Section 9.8 Exercises

363. $(−∞,−5)∪(−1,∞)(−∞,−5)∪(−1,∞)$

365. $[−3,−1][−3,−1]$

367. $(−∞,−6]∪[3,∞)(−∞,−6]∪[3,∞)$

369. $[−3,4][−3,4]$

371.

$(−∞,−4]∪[1,∞)(−∞,−4]∪[1,∞)$

373.

$(2,5)(2,5)$

375.

$(−∞,−5)∪(−3,∞)(−∞,−5)∪(−3,∞)$

377.

$[2−2,2+2][2−2,2+2]$

379.

$(−∞,5−6)∪(5+6,∞)(−∞,5−6)∪(5+6,∞)$

381.

$23, 5223, 52$

383.

$[−12,4][−12,4]$

385.

$(−∞,∞).(−∞,∞).$

387.

no solution

389.

$(−∞,∞).(−∞,∞).$

391.

393.

### Review Exercises

395.

$y=±12y=±12$

397.

$a=±5a=±5$

399.

$r=±42ir=±42i$

401.

$w=±53w=±53$

403.

$p=1,p=9p=1,p=9$

405.

$x=14±34x=14±34$

407.

$n=4±102n=4±102$

409.

$n=−5±23n=−5±23$

411.

$(x+11)2(x+11)2$

413.

$(a−32)2(a−32)2$

415.

$d=−13,−1d=−13,−1$

417.

$m=−3±10im=−3±10i$

419.

$v=7±32v=7±32$

421.

$m=−9,−1m=−9,−1$

423.

$a=32±412a=32±412$

425.

$u=−6±32u=−6±32$

427.

$p=0,6p=0,6$

429.

$y=−12,2y=−12,2$

431.

$c=−13±273c=−13±273$

433.

$x=32±12ix=32±12i$

435.

$x=14,1x=14,1$

437.

$r=−6,7r=−6,7$

439.

$v=−54,1v=−54,1$

441.

$m=−4±103m=−4±103$

443.

$a=512±2312ia=512±2312i$

445.

$u=5±22u=5±22$

447.

$p=4±65p=4±65$

449.

$c=−12c=−12$

451.

1 2 2 0

453.

455.

$x=±2,±23x=±2,±23$

457.

$x=±1,±12x=±1,±12$

459.

$x=16x=16$

461.

$x=64,216x=64,216$

463.

$x=−2,43x=−2,43$

465.

Two consecutive even numbers whose product is 624 are 24 and 26, and −24 and −26.

467.

The height is 14 inches and the width is 10 inches.

469.

The length of the diagonal is 3.6 feet.

471.

The width of the serving table is 4.7 feet and the length is 16.1 feet. 473.

The speed of the wind was 30 mph.

475.

One man takes 3 hours and the other man 6 hours to finish the repair alone.

477. 479.

up down

481.

$x=2;(2,−7)x=2;(2,−7)$

483.

$y:(0,15)x:(3,0),(5,0)y:(0,15)x:(3,0),(5,0)$

485.

$y:(0,−46)x:noney:(0,−46)x:none$

487.

$y:(0,64)x:(−8,0)y:(0,64)x:(−8,0)$

489. 491. 493. 495.

The maximum value is 2 when x = 2.

497.

The length adjacent to the building is 90 feet giving a maximum area of 4,050 square feet.

499. 501. 503. 505. 507. 509.

$f(x)=2(x−1)2−6f(x)=2(x−1)2−6$

511.

$f(x)=3(x−1)2−4f(x)=3(x−1)2−4$ 513.

$f(x)=2(x+1)2+4f(x)=2(x+1)2+4$ 515.

$f(x)=−3(x+2)2+7f(x)=−3(x+2)2+7$ 517.

$f(x)=(x+1)2−5f(x)=(x+1)2−5$

519. $(−∞,−2)∪(3,∞)(−∞,−2)∪(3,∞)$

521. $[−2,1][−2,1]$

523.

$(2,4)(2,4)$

525.

$[3−5,3+5][3−5,3+5]$

527.

no solution

### Practice Test

529.

$w=−2,w=−8w=−2,w=−8$

531.

$m=1,m=32m=1,m=32$

533.

$y=23y=23$

535.

2 complex

537.

$y=1,y=−27y=1,y=−27$

539.

down $x=−4x=−4$
$(−4,0)(−4,0)$ $y:(0,−16);x:(−4,0)y:(0,−16);x:(−4,0)$
maximum value of $00$ when $x=−4x=−4$

541. 543. $f(x)=2(x−1)2−6f(x)=2(x−1)2−6$

545.

$(−∞,−52)∪(2,∞)(−∞,−52)∪(2,∞)$

547.

The diagonal is 4.4 units long.

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