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Be Prepared

10.1

5 3 5 3

10.2

8 3 3 8 3 3

10.3

2 x 3 2 2 x 3 2

10.4

x 2 + 24 x + 144 x 2 + 24 x + 144

10.5

y 9 2 y 9 2

10.6

5 ( n + 4 ) 2 5 ( n + 4 ) 2

10.7

5 2 5 2

10.8

15 15

10.9

8 2 8 2

10.10

51 , 49 51 , 49

10.11

8 8

10.12

13 inches 13 inches

10.14

5 5

10.15

5 4 5 4

Try It

10.1

x = 9 , x = −9 x = 9 , x = −9

10.2

y = 11 , y = −11 y = 11 , y = −11

10.3

x = 5 2 , x = −5 2 x = 5 2 , x = −5 2

10.4

y = 3 3 , y = −3 3 y = 3 3 , y = −3 3

10.5

x = 7 , x = −7 x = 7 , x = −7

10.6

z = 6 , z = −6 z = 6 , z = −6

10.7

no real solution

10.8

no real solution

10.9

x = 2 10 , x = −2 10 x = 2 10 , x = −2 10

10.10

y = 2 7 , y = −2 7 y = 2 7 , y = −2 7

10.11

r = 6 5 5 , r = 6 5 5 r = 6 5 5 , r = 6 5 5

10.12

t = 8 3 3 , t = 8 3 3 t = 8 3 3 , t = 8 3 3

10.13

q = −6 , q = −4 q = −6 , q = −4

10.14

r = 8 , r = −2 r = 8 , r = −2

10.15

a = 3 + 3 2 , a = 3 3 2 a = 3 + 3 2 , a = 3 3 2

10.16

b = −2 + 2 10 , b = −2 2 10 b = −2 + 2 10 , b = −2 2 10

10.17

x = 1 3 + 5 3 , x = 1 3 5 3 x = 1 3 + 5 3 , x = 1 3 5 3

10.18

y = 3 4 + 7 4 , y = 3 4 7 4 y = 3 4 + 7 4 , y = 3 4 7 4

10.19

a = 5 + 2 5 , a = 5 2 5 a = 5 + 2 5 , a = 5 2 5

10.20

b = 3 + 4 2 , b = 3 4 2 b = 3 + 4 2 , b = 3 4 2

10.21

no real solution

10.22

no real solution

10.23

x = 3 + 2 3 , x = 3 2 3 x = 3 + 2 3 , x = 3 2 3

10.24

y = −6 + 4 2 , y = −6 4 2 y = −6 + 4 2 , y = −6 4 2

10.25

m = 1 , m = 7 3 m = 1 , m = 7 3

10.26

n = 3 4 , n = 7 4 n = 3 4 , n = 7 4

10.27

( y + 6 ) 2 ( y + 6 ) 2

10.28

( z + 4 ) 2 ( z + 4 ) 2

10.29

( a 10 ) 2 ( a 10 ) 2

10.30

( b 2 ) 2 ( b 2 ) 2

10.31

( m 5 2 ) 2 ( m 5 2 ) 2

10.32

( n + 13 2 ) 2 ( n + 13 2 ) 2

10.33

( p + 1 8 ) 2 ( p + 1 8 ) 2

10.34

( q 1 3 ) 2 ( q 1 3 ) 2

10.35

c = −5 , c = 1 c = −5 , c = 1

10.36

d = −9 , d = −1 d = −9 , d = −1

10.37

r = −2 , r = 6 r = −2 , r = 6

10.38

t = −1 , t = 11 t = −1 , t = 11

10.39

no real solution

10.40

no real solution

10.41

x = 8 ± 4 3 x = 8 ± 4 3

10.42

y = −4 ± 3 3 y = −4 ± 3 3

10.43

a = −7 , a = 3 a = −7 , a = 3

10.44

b = −10 , b = 2 b = −10 , b = 2

10.45

p = 5 2 ± 61 2 p = 5 2 ± 61 2

10.46

q = 7 2 ± 37 2 q = 7 2 ± 37 2

10.47

c = −3 ± 4 2 c = −3 ± 4 2

10.48

d = −7 , d = 11 d = −7 , d = 11

10.49

m = −4 ± 2 5 m = −4 ± 2 5

10.50

n = −2 , 8 n = −2 , 8

10.51

r = 7 3 , r = 3 r = 7 3 , r = 3

10.52

t = 5 2 , t = 2 t = 5 2 , t = 2

10.53

x = 3 8 ± 201 8 x = 3 8 ± 201 8

10.54

y = 3 10 ± 209 10 y = 3 10 ± 209 10

10.55

y = 2 3 , y = 1 y = 2 3 , y = 1

10.56

z = 3 2 , z = 1 z = 3 2 , z = 1

10.57

a = −3 , a = 5 a = −3 , a = 5

10.58

b = −6 , b = −4 b = −6 , b = −4

10.59

p = −4 ± 6 2 p = −4 ± 6 2

10.60

q = 11 ± 61 10 q = 11 ± 61 10

10.61

m = −6 ± 15 3 m = −6 ± 15 3

10.62

n = −2 ± 2 6 5 n = −2 ± 2 6 5

10.63

no real solution

10.64

no real solution

10.65

x = −1 ± 6 x = −1 ± 6

10.66

y = 2 3 , y = 1 y = 2 3 , y = 1

10.67

c = 2 ± 7 3 c = 2 ± 7 3

10.68

d = 3 , d = 3 2 d = 3 , d = 3 2

10.69

r = −5 r = −5

10.70

t = 4 5 t = 4 5

10.71

no real solutions 2 1 no real solutions

10.72

2 no real solutions 1 2

10.73

factor Square Root Property Quadratic Formula

10.74

Quadratic Formula factoring Square Root Property

10.75

Two consecutive odd numbers whose product is 99 are 9 and 11, and −9−9 and −11−11.

10.76

Two consecutive even numbers whose product is 168 are 12 and 14,and −12−12 and −14−14.

10.77

The height of the triangle is 8 inches and the width is 52 inches.

10.78

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

10.79

The length of the shadow is 6.3 feet and the length of the flag pole is 18.9 ft.

10.80

The distance to the opposite corner is 3.2.

10.81

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

10.82

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

10.83

The arrow will reach 180 on its way up in 3 seconds, and on the way down in 3.8 seconds.

10.84

The ball will reach 48 feet on its way up in .6 seconds and on the way down in 5.5 seconds.

10.87

up down

10.88

down up

10.89

x=2x=2 (2,−7)(2,−7)

10.90

x=1x=1 (1,−5)(1,−5)

10.91

y : ( 0 , −8 ) ; x : ( −4 , 0 ) , ( 2 , 0 ) y : ( 0 , −8 ) ; x : ( −4 , 0 ) , ( 2 , 0 )

10.92

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

10.93

y : ( 0 , 4 ) ; x : none y : ( 0 , 4 ) ; x : none

10.94

y : ( 0 , −5 ) ; x : ( 5 , 0 ) ( −1 , 0 ) y : ( 0 , −5 ) ; x : ( 5 , 0 ) ( −1 , 0 )

10.95

y : ( 0 , −36 ) ; x : ( −6 , 0 ) y : ( 0 , −36 ) ; x : ( −6 , 0 )

10.96

y : ( 0 , 4 ) ; x : ( 2 3 , 0 ) y : ( 0 , 4 ) ; x : ( 2 3 , 0 )

10.97

y:(0,−8)y:(0,−8); x:(2,0),(−4,0)x:(2,0),(−4,0);
axis: x=−1x=−1; vertex: (−1,−9)(−1,−9);

The graph shows an upward-opening parabola graphed on the x y-coordinate plane. The x-axis of the plane runs from -10 to 10. The y-axis of the plane runs from -10 to 10. The vertex is at the point (-1, -9). Three points are plotted on the curve at (0, -8), (2, 0) and (-4, 0). Also on the graph is a dashed vertical line representing the axis of symmetry. The line goes through the vertex at x equals -1.
10.98

y:(0,12);x:(2,0),(6,0);y:(0,12);x:(2,0),(6,0);
axis: x=4;vertex:(4,−4)x=4;vertex:(4,−4);

The graph shows an upward-opening parabola graphed on the x y-coordinate plane. The x-axis of the plane runs from -10 to 10. The y-axis of the plane runs from -10 to 10. The vertex is at the point (4, -4). Three points are plotted on the curve at (0, 12), (2, 0) and (6, 0). Also on the graph is a dashed vertical line representing the axis of symmetry. The line goes through the vertex at x equals 4.
10.99

y:(0,−12);x:(2,0);y:(0,−12);x:(2,0);
axis: x=2;vertex:(2,0)x=2;vertex:(2,0);

The graph shows an downward-opening parabola graphed on the x y-coordinate plane. The x-axis of the plane runs from -10 to 10. The y-axis of the plane runs from -1 to 10. The vertex is at the point (2, 0). One other point is plotted on the curve at (0, -12). Also on the graph is a dashed vertical line representing the axis of symmetry. The line goes through the vertex at x equals 2.
10.100

y:(0,1);x:(15,0);y:(0,1);x:(15,0);
axis: x=15;vertex:(15,0)x=15;vertex:(15,0);

The graph shows an upward-opening parabola graphed on the x y-coordinate plane. The x-axis of the plane runs from -5 to 5. The y-axis of the plane runs from -5 to 10. The vertex is at the point (-1 fifth, 0). One other point is plotted on the curve at (0, 1). Also on the graph is a dashed vertical line representing the axis of symmetry. The line goes through the vertex at x equals -1 fifth.
10.101

y:(0,5);x:none;y:(0,5);x:none;
axis: x=32;vertex:(32,12)x=32;vertex:(32,12);

The graph shows an upward-opening parabola graphed on the x y-coordinate plane. The x-axis of the plane runs from -5 to 5. The y-axis of the plane runs from -5 to 10. The vertex is at the point (3 halves, 1 half). One other point is plotted on the curve at (0, 5). Also on the graph is a dashed vertical line representing the axis of symmetry. The line goes through the vertex at x equals 3 halves.
10.102

y:(0,−1);x:none;y:(0,−1);x:none;
axis: x=0;vertex:(0,−1)x=0;vertex:(0,−1);

The graph shows an upward-opening parabola graphed on the x y-coordinate plane. The x-axis of the plane runs from -10 to 10. The y-axis of the plane runs from -10 to 10. The vertex is at the point (0, -1). Also on the graph is a dashed vertical line representing the axis of symmetry. The line goes through the vertex at x equals 0.
10.103

y:(0,3);x:(−1.6,0),(−0.4,0);y:(0,3);x:(−1.6,0),(−0.4,0);
axis: x=−1;vertex:(−1,−2)x=−1;vertex:(−1,−2);

The graph shows an upward-opening parabola graphed on the x y-coordinate plane. The x-axis of the plane runs from -5 to 5. The y-axis of the plane runs from -5 to 5. The vertex is at the point (-1,-2). Three other points are plotted on the curve at (0, 3), (-1.6, 0), (-0.4, 0). Also on the graph is a dashed vertical line representing the axis of symmetry. The line goes through the vertex at x equals -1.
10.104

y:(0,5);x:(0.6,0),(−2.6,0);y:(0,5);x:(0.6,0),(−2.6,0);
axis: x=−1;vertex:(−1,8)x=−1;vertex:(−1,8);

The graph shows an downward-opening parabola graphed on the x y-coordinate plane. The x-axis of the plane runs from -10 to 10. The y-axis of the plane runs from -10 to 10. The vertex is at the point (-1, 8). Three other points are plotted on the curve at (0, 5), (0.6, 0) and (-2.6, 0). Also on the graph is a dashed vertical line representing the axis of symmetry. The line goes through the vertex at x equals -1.
10.105

The minimum value is −4−4 when x=4x=4.

10.106

The maximum value is 5 when x=2x=2.

10.107

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

10.108

It will take 6.5 seconds to reach the maximum height of 676 feet.

Section 10.1 Exercises

1.

a = ± 7 a = ± 7

3.

r = ± 2 6 r = ± 2 6

5.

u = ± 10 3 u = ± 10 3

7.

m = ± 3 m = ± 3

9.

no real solution

11.

a = ± 2 5 a = ± 2 5

13.

p = ± 4 7 7 p = ± 4 7 7

15.

x = 1 , x = −5 x = 1 , x = −5

17.

u = 14 , u = −2 u = 14 , u = −2

19.

m = 6 ± 2 5 m = 6 ± 2 5

21.

r = 1 2 ± 3 2 r = 1 2 ± 3 2

23.

a = 7 ± 5 2 a = 7 ± 5 2

25.

no real solution

27.

m = 2 ± 2 2 m = 2 ± 2 2

29.

x = 3 5 , x = 9 5 x = 3 5 , x = 9 5

31.

r = ± 4 r = ± 4

33.

a = 4 ± 2 7 a = 4 ± 2 7

35.

w = 1 , w = 5 3 w = 1 , w = 5 3

37.

a = ± 3 2 a = ± 3 2

39.

p = 1 3 ± 7 3 p = 1 3 ± 7 3

41.

no real solution

43.

u = 7 ± 6 2 u = 7 ± 6 2

45.

m = 4 ± 2 3 m = 4 ± 2 3

47.

x = −3 , x = −7 x = −3 , x = −7

49.

c = ± 5 6 6 c = ± 5 6 6

51.

no real solution

53.

4 feet

55.

Answers will vary.

Section 10.2 Exercises

57.

( a + 5 ) 2 ( a + 5 ) 2

59.

( m + 9 ) 2 ( m + 9 ) 2

61.

( m 12 ) 2 ( m 12 ) 2

63.

( p 11 ) 2 ( p 11 ) 2

65.

( x 9 2 ) 2 ( x 9 2 ) 2

67.

( p 1 6 ) 2 ( p 1 6 ) 2

69.

v = −10 , v = 4 v = −10 , v = 4

71.

u = −3 , u = 1 u = −3 , u = 1

73.

c = −1 , c = 13 c = −1 , c = 13

75.

x = −1 , x = 21 x = −1 , x = 21

77.

no real solution

79.

no real solution

81.

a = 5 ± 2 5 a = 5 ± 2 5

83.

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

85.

v = 9 2 ± 89 2 v = 9 2 ± 89 2

87.

x = −7 , x = 3 x = −7 , x = 3

89.

m = −11 , m = 1 m = −11 , m = 1

91.

c = −2 , c = 3 2 c = −2 , c = 3 2

93.

p = 7 4 ± 161 4 p = 7 4 ± 161 4

95.

16 feet, 20 feet

97.

−5−5 −5−5 Answers will vary.

Section 10.3 Exercises

99.

m = −1 , m = 3 4 m = −1 , m = 3 4

101.

p = 1 2 , p = 3 p = 1 2 , p = 3

103.

p = −4 , p = −3 p = −4 , p = −3

105.

r = −3 , r = 11 r = −3 , r = 11

107.

u = −7 ± 73 6 u = −7 ± 73 6

109.

a = 3 ± 3 2 a = 3 ± 3 2

111.

no real solution

113.

v = −5 ± 65 2 v = −5 ± 65 2

115.

m = −1 , m = 3 4 m = −1 , m = 3 4

117.

c = 3 4 c = 3 4

119.

m = 7 5 , m = 1 m = 7 5 , m = 1

121.

p = −3 , p = 9 p = −3 , p = 9

123.

r = −3 ± 89 8 r = −3 ± 89 8

125.

a = −6 ± 26 2 a = −6 ± 26 2

127.

b = −2 ± 22 6 b = −2 ± 22 6

129.

x = −6 ± 42 4 x = −6 ± 42 4

131.

no real solutions 1
2 no real solutions

133.

1 no real solutions
1 2

135.

factor square root
Quadratic Formula

137.

square root square root
factor

139.

5 seconds, 8 seconds

141.

−20,10−20,10 −20,10−20,10
answers will vary

Section 10.4 Exercises

143.

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

145.

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

147.

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

149.

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

151.

The leg of the right triangle is 1.7 feet and the hypotenuse is 3.4 feet.

153.

The length of the diagonal of the fence is 7.3 yards.

155.

The width of the driveway is 10 feet and its length is 35 feet.

157.

The rocket will reach 1,200 feet on its way up in 2 seconds and on the way down in 38 seconds.

159.

70 seconds

161.

answers will vary
answers will vary answers will vary answers will vary

Section 10.5 Exercises

163.
This figure shows an upward-opening parabola graphed on the x y-coordinate plane. The x-axis of the plane runs from -10 to 10. The y-axis of the plane runs from -10 to 10. The parabola has a vertex at (0, 3) and goes through the point (1, 4).
165.

down

167.

up

169.

x=−4x=−4 (−4,−17)(−4,−17)

171.

x=1x=1 (1,6)(1,6)

173.

y : ( 0 , 6 ) ; x : ( −1 , 0 ) , ( −6 , 0 ) y : ( 0 , 6 ) ; x : ( −1 , 0 ) , ( −6 , 0 )

175.

y : ( 0 , 19 ) ; x : none y : ( 0 , 19 ) ; x : none

177.

y : ( 0 , 25 ) ; x : ( 5 2 , 0 ) y : ( 0 , 25 ) ; x : ( 5 2 , 0 )

179.

y:(0,5);x:(−1,0),(−5,0);y:(0,5);x:(−1,0),(−5,0);
axis: x=−3;vertex:(−3,−4)x=−3;vertex:(−3,−4)

This figure shows an upward-opening parabola graphed on the x y-coordinate plane. The x-axis of the plane runs from -10 to 10. The y-axis of the plane runs from -10 to 10. The parabola has points plotted at the vertex (-3, -4) and the intercepts (-5, 0), (-1, 0) and (0, 5). Also on the graph is a dashed vertical line representing the axis of symmetry. The line goes through the vertex at x equals -3.
181.

y:(0,3);x:(−1,0),(−3,0);y:(0,3);x:(−1,0),(−3,0);
axis: x=−2;vertex:(−2,−1)x=−2;vertex:(−2,−1)

This figure shows an upward-opening parabola graphed on the x y-coordinate plane. The x-axis of the plane runs from -10 to 10. The y-axis of the plane runs from -10 to 10. The parabola has points plotted at the vertex (-2, -1) and the intercepts (-1, 0), (-3, 0) and (0, 3). Also on the graph is a dashed vertical line representing the axis of symmetry. The line goes through the vertex at x equals -2.
183.

y:(0,4)x:(23,0);y:(0,4)x:(23,0);
axis: x=23;vertex:(23,0)x=23;vertex:(23,0)

This figure shows an upward-opening parabola graphed on the x y-coordinate plane. The x-axis of the plane runs from -5 to 5. The y-axis of the plane runs from -5 to 5. The parabola has points plotted at the vertex (-2 thirds, 0) and the intercept (0, 4). Also on the graph is a dashed vertical line representing the axis of symmetry. The line goes through the vertex at x equals -2 thirds.
185.

y:(0,−7);x:none;y:(0,−7);x:none;
axis: x=1;vertex:(1,−6)x=1;vertex:(1,−6)

This figure shows a downward-opening parabola graphed on the x y-coordinate plane. The x-axis of the plane runs from -10 to 10. The y-axis of the plane runs from -15 to 5. The parabola has points plotted at the vertex (1, -6) and the intercept (0, -7). Also on the graph is a dashed vertical line representing the axis of symmetry. The line goes through the vertex at x equals 1.
187.

y:(0,1);x:(1.7,0),(0.3,0);y:(0,1);x:(1.7,0),(0.3,0);
axis: x=1;vertex:(1,−1)x=1;vertex:(1,−1)

This figure shows an upward-opening parabola graphed on the x y-coordinate plane. The x-axis of the plane runs from -10 to 10. The y-axis of the plane runs from -10 to 10. The parabola has points plotted at the vertex (1, -1) and the intercepts (1.7, 0), (0.3, 0) and (0, 1). Also on the graph is a dashed vertical line representing the axis of symmetry. The line goes through the vertex at x equals 1.
189.

y:(0,2)x:(1,0);y:(0,2)x:(1,0);
axis: x=1;vertex:(1,0)x=1;vertex:(1,0)

 This figure shows an upward-opening parabola graphed on the x y-coordinate plane. The x-axis of the plane runs from -10 to 10. The y-axis of the plane runs from -10 to 10. The parabola has points plotted at the vertex (1, 0) and the intercept (0, 2). Also on the graph is a dashed vertical line representing the axis of symmetry. The line goes through the vertex at x equals 1.
191.

y:(0,2)x:(−4.4,0),(0.4,0);y:(0,2)x:(−4.4,0),(0.4,0);
axis: x=−2;vertex:(−2,6)x=−2;vertex:(−2,6)

This figure shows a downward-opening parabola graphed on the x y-coordinate plane. The x-axis of the plane runs from -10 to 10. The y-axis of the plane runs from -10 to 10. The parabola has points plotted at the vertex (-2, 6) and the intercepts (-4.4, 0), (0.4, 0) and (0, 2). Also on the graph is a dashed vertical line representing the axis of symmetry. The line goes through the vertex at x equals -2.
193.

y:(0,8);x:none;y:(0,8);x:none;
axis: x=1;vertex:(1,3)x=1;vertex:(1,3)

This figure shows an upward-opening parabola graphed on the x y-coordinate plane. The x-axis of the plane runs from -10 to 10. The y-axis of the plane runs from -10 to 10. The parabola has points plotted at the vertex (1, 3) and the intercept(0, 8). Also on the graph is a dashed vertical line representing the axis of symmetry. The line goes through the vertex at x equals 1.
195.

y:(0,20)x:(−4.5,0),(−1.5,0);y:(0,20)x:(−4.5,0),(−1.5,0);
axis: x=−3;vertex:(−3,−7)x=−3;vertex:(−3,−7)

This figure shows an upward-opening parabola graphed on the x y-coordinate plane. The x-axis of the plane runs from -10 to 10. The y-axis of the plane runs from -10 to 10. The parabola has points plotted at the vertex (-3, -7) and the intercepts (-4.5, 0) and (-1.5, 0). Also on the graph is a dashed vertical line representing the axis of symmetry. The line goes through the vertex at x equals -3.
197.

The minimum value is 9898 when x=14x=14.

199.

The minimum value is 6 when x=3x=3.

201.

The maximum value is 16 when x=0x=0.

203.

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

205.

Charging $20 for each computer will give the maximum revenue of $400.

207.

The length of the side along the river of the corral is 60 feet and the maximum area is 7,200 sq ft.

209.

  1. This figure shows a downward-opening parabola graphed on the x y-coordinate plane. The x-axis of the plane runs from -10 to 60. The y-axis of the plane runs from -50 to 500. The parabola has a vertex at (20, 400) and also goes through the points (0, 0) and (40, 0).
  2. (0,0),(40,0)(0,0),(40,0)
211.

Answers will vary.

Review Exercises

213.

x = ± 10 x = ± 10

215.

m = ± 2 10 m = ± 2 10

217.

a = ± 5 a = ± 5

219.

no solution

221.

v = ± 3 2 v = ± 3 2

223.

c = ± 4 5 5 c = ± 4 5 5

225.

p = 1 , 9 p = 1 , 9

227.

u = −1 ± 3 5 u = −1 ± 3 5

229.

x = 1 4 ± 3 4 x = 1 4 ± 3 4

231.

m = 7 ± 2 6 m = 7 ± 2 6

233.

no solution

235.

m = 3 ± 4 3 m = 3 ± 4 3

237.

a = 3 2 , 3 4 a = 3 2 , 3 4

239.

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

241.

( m 4 ) 2 ( m 4 ) 2

243.

( a 3 2 ) 2 ( a 3 2 ) 2

245.

( p + 2 5 ) 2 ( p + 2 5 ) 2

247.

c = 1 , −21 c = 1 , −21

249.

x = −4 , 8 x = −4 , 8

251.

no solution

253.

v = 7 ± 3 2 v = 7 ± 3 2

255.

m = −9 , −1 m = −9 , −1

257.

a = 3 2 ± 41 2 a = 3 2 ± 41 2

259.

u = −6 ± 3 2 u = −6 ± 3 2

261.

p = 0 , 6 p = 0 , 6

263.

y = 1 2 , 2 y = 1 2 , 2

265.

c = 1 3 ± 2 7 3 c = 1 3 ± 2 7 3

267.

x = 1 4 , 1 x = 1 4 , 1

269.

r = −6 , 7 r = −6 , 7

271.

v = 5 4 , 1 v = 5 4 , 1

273.

m = −4 ± 10 3 m = −4 ± 10 3

275.

no real solution

277.

u = 5 ± 22 u = 5 ± 22

279.

p = 4 ± 6 5 p = 4 ± 6 5

281.

c = 1 2 c = 1 2

283.

1 2 2 none

285.

factor Quadratic Formula square root

287.

Two consecutive odd numbers whose product is 323 are 17 and 19, and −17−17 and −19.−19.

289.

The height of the banner is 13 cm and the length of the side is 54 cm.

291.

The lengths of the sides of the mosaic are 2.2 and 4.4 feet.

293.

The width of the front walk is 8.2 feet and its length is 30.6 feet.

295.

The ball will reach 384 feet on its way up in 4 seconds and on the way down in 6 seconds.

297.
This figure shows an upward-opening parabola graphed on the x y-coordinate plane. The x-axis of the plane runs from -10 to 10. The y-axis of the plane runs from -10 to 10. The parabola has a vertex at (0, -2) and goes through the point (1, -1).
299.

down

301.

up

303.

x=3x=3 (3,17)(3,17)

305.

y : ( 0 , 5 ) ; x : ( 5 , 0 ) , ( −1 , 0 ) y : ( 0 , 5 ) ; x : ( 5 , 0 ) , ( −1 , 0 )

307.

y : ( 0 , 10 ) ; x : none y : ( 0 , 10 ) ; x : none

309.

y : ( 0 , 1 ) ; x : ( 1 4 , 0 ) y : ( 0 , 1 ) ; x : ( 1 4 , 0 )

311.

y:(0,15);x:(−3,0),(−5,0);y:(0,15);x:(−3,0),(−5,0);
axis: x=−4;vertex:(−4,−1)x=−4;vertex:(−4,−1)

This figure shows an upward-opening parabola graphed on the x y-coordinate plane. The x-axis of the plane runs from -10 to 10. The y-axis of the plane runs from -2 to 17. The parabola has points plotted at the vertex (-4, -1) and the intercepts (-3, 0), (-5, 0) and (0, 15). Also on the graph is a dashed vertical line representing the axis of symmetry. The line goes through the vertex at x equals -4.
313.

y:(0,−16);x:(4,0);y:(0,−16);x:(4,0);
axis: x=4;vertex:(4,0)x=4;vertex:(4,0)

This figure shows a downward-opening parabola graphed on the x y-coordinate plane. The x-axis of the plane runs from -15 to 12. The y-axis of the plane runs from -20 to 2. The parabola has points plotted at the vertex (4, 0) and the intercept (0, -16). Also on the graph is a dashed vertical line representing the axis of symmetry. The line goes through the vertex at x equals 4.
315.

y:(0,13);x:none;y:(0,13);x:none;
axis: x=−3;vertex:(−3,4)x=−3;vertex:(−3,4)

This figure shows an upward-opening parabola graphed on the x y-coordinate plane. The x-axis of the plane runs from -10 to 10. The y-axis of the plane runs from -2 to 18. The parabola has points plotted at the vertex (-3, 4) and the intercept (0, 13). Also on the graph is a dashed vertical line representing the axis of symmetry. The line goes through the vertex at x equals -3.
317.

y:(0,−11)x:(3.1,0),(0.9,0);y:(0,−11)x:(3.1,0),(0.9,0);
axis: x=2;vertex:(2,5)x=2;vertex:(2,5)

This figure shows a downward-opening parabola graphed on the x y-coordinate plane. The x-axis of the plane runs from -10 to 10. The y-axis of the plane runs from -10 to 10. The parabola has points plotted at the vertex (2, 5) and the intercepts (3.1, 0) and (0.9, 0). Also on the graph is a dashed vertical line representing the axis of symmetry. The line goes through the vertex at x equals 2.
319.

The minimum value is −1−1 when x=−1x=−1.

321.

In 3.5 seconds the ball is at its maximum height of 196 feet.

Practice Test

323.

w = −2 , −8 w = −2 , −8

325.

m = 1 , 3 2 m = 1 , 3 2

327.

n = −4 ± 7 3 n = −4 ± 7 3

329.

no real solution

331.

2

333.

Two consecutive even number are −20−20 and −18−18 and 18 and 20.

335.

up x=−1x=−1 (−1,5)(−1,5) y:(0,8);x:noney:(0,8);x:none minimum value of 5 when x=−1x=−1

337.

up x=−5x=−5 (−5,−1)(−5,−1) y;(0,24);x:(−6,0),(−4,0)y;(0,24);x:(−6,0),(−4,0) minimum value of −1−1 when x=−5x=−5

339.

down x=−4x=−4
(−4,32)(−4,32) y;(0,16);x:(−9.7,0),(1.7,0)y;(0,16);x:(−9.7,0),(1.7,0)
maximum value of 3232 when x=−4x=−4

341.

y:(0,9);x:(34,0);y:(0,9);x:(34,0);
axis: x=34;vertex:(34,0)x=34;vertex:(34,0)

This figure shows an upward-opening parabola graphed on the x y-coordinate plane. The x-axis of the plane runs from -10 to 10. The y-axis of the plane runs from -10 to 10. The parabola has points plotted at the vertex (3 fourths, 0) and the intercept (0, 9). Also on the graph is a dashed vertical line representing the axis of symmetry. The line goes through the vertex at x equals 3 fourths.
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