Beginning Algebra, 11th Edition

57. ; Only 16 ft is a reasonable answer. 59.


58. 
    
    
    
    63. 
        
    
    
    
    

Summary Exercises on Quadratic Equations
(pages 573–574)

1. 
   
   
   
   2. 
      
      
      
      3. 
         
         
         
         4. 
            
            
            
            5. 
               
            
            
            
            
         
         
         
         
      
      
      
      
   
   
   
   


2. 
   
   
   
   7. 
      
      
      
      8. 
         
         
         
         9. 
            
         
         
         
         
      
      
      
      
   
   
   
   


3. 
   
   
   
   11. 
       
       
       
       12. 
           
           
           
           13. 
               
           
           
           
           
       
       
       
       
   
   
   
   


4. 
   
   
   
   15. 
       
       
       
       16. 
           
           
           
           17. 
               
               
               
               18. 
                   
               
               
               
               
           
           
           
           
       
       
       
       
   
   
   
   


5. 
   
   
   
   20. 
       
       
       
       21. 
           
           
           
           22. 
               
           
           
           
           
       
       
       
       
   
   
   
   


6. 
   
   
   
   24. 
       
       
       
       25. 
           
           
           
           26. 
               
           
           
           
           
       
       
       
       
   
   
   
   


7. 
   
   
   
   28. 
       
       
       
       29. 
           
       
       
       
       
   
   
   
   


8. 
   
   
   
   31. 
       
       
       
       32. 
           
       
       
       
       
   
   
   
   


9. 
   
   
   
   34. 
       
       
       
       35. 
           
           
           
           36. 
               
               
               
               37. 
                   
               
               
               
               
           
           
           
           
       
       
       
       
   
   
   
   


10. 
    
    
    
    39. 
        
        
        
        40. 
            
            
            
            41. 
                
                
                
                42. 
                    
                
                
                
                
            
            
            
            
        
        
        
        
    
    
    
    

Section 9.4 (pages 579–580)

1. 3 i 3. 5. 7. 9. 11.


2. 
   
   
   
   15. 
       
       
       
       17. 
           
           
           
           19. 
               
               
               
               21. 
                   
               
               
               
               
           
           
           
           
       
       
       
       
   
   
   
   


3. 
   
   
   
   25. 
       
       
       
       27. 
           
           
           
           29. 45 31.
           
           
           
           
       
       
       
       
   
   
   
   


4. 
   
   
   
   35. 
       
       
       
       37. 
           
           
           
           39. 
               
               
               
               41. 
                   
               
               
               
               
           
           
           
           
       
       
       
       
   
   
   
   


5. 
   
   
   
   45. 
       
       
       
       47. 
           
           
           
           49. 
               
           
           
           
           
       
       
       
       
   
   
   
   


6. 
   
   
   
   53. 
       
       
       
       55. 
           
       
       
       
       
   
   
   
   


7. 
   
   
   
   59. 61.true
   
   
   
   

63.false; For example, is a complex number but it is not real.

65. 
    
    
    
    67. 16
    
    
    
    

Section 9.5 (pages 585–587)

1. 
   
   
   
   3. 
      
      
      
      5. 
         
      
      
      
      
   
   
   
   

x

y

6

3

–3 01

y = x^2 + 2x + 3

x

y

9

4

–6–3 0

y = (x + 3)^2

x

y

–3 0 3

3

–6

y = x^2 – 6

1 0, - 62 1 - 3, 0 2 1 - 1, 2 2

xx

yy

00

33

22 x x – 3– 3y y = 6= 6

–2–2

3 + 2 i

e^1

2

^211

2

e-^1 if

2

^213

2

if

e

1

5 

214

e 5 if

3

2 

27

e- 2 if

3

4 

231

4 if

5 - 1  2 i 6 E 3 i 25 F E- 32 i 22 F 51 i 6

1

2 +

2

• 2 + 5 i 3 - i 3 i
  3
  25 +

4

2 - 6 i 25 i

1

2 +

1

6 + 8 i 14 + 5 i 7 - 22 i 2 i

• 6 + 2 i - 8 + 6 i 6 - 7 i - 2 - 6

2 i 25 3 i 22 5 i 25 5 + 3 i 6 - 9 i

E-^14 ,^23 F E-4, 53 F^5 - 3, 5^6 E-^23 ,^25 F E^109 F

e E-^83 , - 56 F (^00) E-^23 , 2F
8  822
3
f
e-^5 ^25
2
e-^7 ^25 f
4
e-^5 ^241 f
8
f
e

• 2  211
  3
  e f
  1  23
  2
  E^14 , 1F f

e E-^54 F

• 3  241
  2
  E^25 , 4F E- 3  25 F f

e-^5 ^213

6

E-^54 , 23 F E-3,^13 F E^1 ^22 F f

e 0 0 E-^12 , 2F E- 21 , 1F

1  422

7 f

e^7 ^226

3

e^1 ^2105 - 17, 5 (^6) E- 57 , 1F f
2
f
e E-^13 ,^53 F

• 3  217
  2
  5 - 2, - 16 5 4, 5 6 f

e-^3 ^255 - 4, 6 (^6) E (^79) F 5 1, 3 6
2
5  66 f

• 2 + 3 k 24 - 2 r- 15 r^2

5 16, - 86 - 5 + 8 z 7. 9. 11.

13.one real solution; 15.two real solutions; 17.no real

solutions; 19.If , it opens upward, and if , it opens

downward. 21. In Exercises 23–27, we give the domain first,

and then the range. 23. ; 25. ;

27. ; 29. 3 31. 21 33.40 and 40 35.
    37.In each case, there is a vertical “stretch” of the parabola. It becomes
    narrower as the coefficient gets larger. 38.In each case, there is a
    vertical “shrink” of the parabola. It becomes wider as the coefficient gets
    smaller. 39.The graph of is obtained by reflecting the graph of
    across the x-axis. 40.When the coefficient of is negative, the
    parabola opens downward. 41.By adding a positive constant k, the graph
    is shifted kunits upward. By subtracting a positive constant k, the graph
    is shifted kunits downward. 42.Adding a positive constant kbefore
    squaring moves the graph kunits to the left. Subtracting a positive
    constant kbefore squaring moves the graph kunits to the right.

Chapter 9 Review Exercises (pages 591–593)

1. 
   
   
   
   2. 
      
      
      
      3. 
         
         
         
         4. 
            
            
            
            5. 
               
            
            
            
            
         
         
         
         
      
      
      
      
   
   
   
   


2. 
   
   
   
   7. 
      
      
      
      8. 
         
         
         
         9. 
            
         
         
         
         
      
      
      
      
   
   
   
   


3. 
   
   
   
   11. 
       
       
       
       12. 
           
       
       
       
       
   
   
   
   


4. 
   
   
   
   14. 15.2.5 sec 16.6, 8, 10 17. , or
   
   
   
   


5. (a) (b) (c) (d)Because there is only one
   solution set, we will always get the same results, no matter which method

of solution is used. 19. 20. 21.

22. 
    
    
    
    23. 
        
        
        
        24. 25.There are no real solutions. 26. 27. 28. 20
        
        
        
        
    
    
    
    


23. 13 30.i 31. 32.a(the real number itself )
    33.No, the product will always be the
    sum of the squares of two real numbers, which is a real number.


24. 
    
    
    
    35. 
        
        
        
        36. 
            
        
        
        
        
    
    
    
    


25. 
    
    
    
    38. 39.e-^1
        9
        ^222
        9
        e^3 if
        8
        ^223
        8
        e-^3 if
        2
        ^223
        2
        if
    
    
    
    

e^1

3

^22

3

e^2 if

3

^222

3

E-^2 i^23 F^ if

1 a+bi 21 a-bi 2 =a^2 +b^2

28

13 -

3

13 i

5 - i - 6 - 5 i

e E-^23 , 1F

• 3  241
  e 2 f


• 1  229
  4 f

e

2  210

E 1  25 F 0 2 f

5  36 5  36 5  36

9

A 4

3

2 B

E-^202

5 , 1F

e

• 4  222
  2
  E- 2  211 F E- 1  26 F f

e 5 - 5, - 16

3  222

e 0 5 f

• 1  214
  2 f

5  126 E 237 F E 822 F 5 - 7, 3 6 E 3  210 F

Y 1 x^2

Y 2

1 - q, q 23 1, q 2 y= 562511 x^2

1 - q, q 23 0, q 2 1 - q, q 21 - q, 4 4

5 - 2, 3 6

0 a 70 a 60

526 5  26

x

y

0

4

–4

–4 4

y = x^2 + 4x

x

y

0

4

–5

36

x y = –x (^2) + 6x – 5
y
0
4
9
48
y = x^2 – 8x + 16
1 4, 0 2 1 3, 4 2 1 - 2, - 42
Answers to Selected Exercises A-23
40.
x
y
–6
–2 2
y = –3x^2
1 0, 0 2 41.
x
y
–2 02
5
–4
y = –x^2 + 5
1 0, 5 2 42.
x
9 y
4
y = (x–4 + 4)^20
1 - 4, 0 2