Intermediate Algebra (11th edition)

A-22 Answers to Selected Exercises

27.vertex: 4, 0 ;
axis:
domain:
range:

29.vertex:

axis:

domain:

range:

31.vertex:

axis:

domain:

range:

y

0 x

4

2

–4

f(x) = 2 (x– 2)^2 – 4

3 - 4,q 2

1 - q,q 2 ;

x=2;

1 2,- 42 ;

3

y

x

0

–1

–2

f(x) = (x+ 2)^2 – 1

3 - 1,q 2

1 - q,q 2 ;

x=-2;

1 - 2,-1);

y

0 x

2

4

f(x) = (x– 4)^2

3 0,q 2

1 - q,q 2 ;

x=4;

1 2

33.vertex:
axis:
domain:
range:

35.vertex:

axis:

domain:

range:

37.linear; positive

39.quadratic; positive

41.quadratic; negative

43. (a)

x

y

–3

0

2

5

f(x) = 2(x – 2)^2 – 3

3 - 3,q 2

1 - q,q 2 ;

x=2;

1 2,- 32 ;

y

x

–6

–1 0

2

f(x) = – (^12 x+ 1)^2 + 2

1 - q, 2 4

1 - q,q 2 ;

x=-1;

1 - 1, 2 2 ;

(b)quadratic; positive (c)
(d)$9496 million (e)No. The number of digital cameras sold in 2007
is far below the number approximated by the model. Rather than continu-
ing to increase, sales of digital cameras fell in 2007. 45. (a) 6105
(b)The approximation using the model is low. 47.

49. 
    
    
    
    51. 
        
        
        
        53. 
            
        
        
        
        
    
    
    
    

Section 9.6 (pages 548–551)

1.Ifxis squared, it has a vertical axis. If yis squared, it has a horizontal
axis. 3.Use the discriminant of the function. If it is positive, there are

two x-intercepts. If it is 0, there is one x-intercept (at the vertex), and if it
is negative, there is no x-intercept. 5. 7.

9. 
   
   
   
   11. up; narrower; no x-intercepts
   
   
   
   


10. down; same; two x-intercepts 15. to the right;

wider 17.F 19.C 21.D

A^52 ,^374 B;^1 - 3,-^92 ;

A-^12 ,-^294 B^1 - 1, 3^2 ;

1 - 4,- 62 1 1,- 32

• 2 5 - 4, 1 6 E- 3  223 F

5 - 4, 5 6

ƒ 1 x 2 =99.3x^2 +400.7x+ 1825

Years Since 2000

1000

2000

3000

4000

8000

7000

(^0123456)
y
x
6000
5000
Sales (in millions of dollars)
23.vertex:
axis: ;
domain:
range:
25.vertex:
axis: ;
domain:
range:
27.vertex:
axis: ;
domain:
range:
x
y
0
–2
15
x = (y+ 2)^2 + 1
1 - q,q 2
3 1,q 2 ;
y=- 2
1 1,- 22 ;
–5
x
y
01
–3
f(x) = –2x^2 + 4x – 5
1 - q,- 34
1 - q,q 2 ;
x= 1
1 1,- 32 ;
x
y
0
–6
–4
3
f(x) = x^2 + 8x + 10
3 - 6,q 2
1 - q,q 2 ;
x=- 4
1 - 4,- 62 ;
33.20 and 20 35.140 ft by 70 ft; 9800 37.16 ft; 2 sec
39.2 sec; 65 ft 41.20 units; $210 43. (a)minimum
(b)2003; $825.8 billion 45. (a)The coefficient of is negative
because a parabola that models the data must open down.
(b) 18.45, 3860 (c)In 2018 Social Security assets will reach
theirmaximum value of $3860 billion.

47. (a)
    (b) (c) 25 (d)$22,500
    49.

51.

53.

Section 9.7 (pages 557–558)

1. (a) 1, 3 (b) (c)


2. (a) (b) (c)


3. 
   

7.

9.

11.

13.

15.

17.

19.

21.

23. 
    
    
    
    25. 
        
        
        
        27. 
            
        
        
        
        
    
    
    
    

29.

31.

33. 
    
    
    
    35. 2, 6
    
    
    
    

37.

39.

41.

042

1 - q, 2 2 ́ 1 4,q 2

–7 –2 0

3 - 7,- 22

1

2

5

(^024)
A-q,^12 B ́A^54 ,qB
0 2 6
1 4

-^3205

C-^32 , 5B

041

1 - q, 1 2 ́ 1 4,q 2

3

• 2
  1
  03 2 4

C-^32 ,^13 D ́ 3 4,q 2

041 2

1 - q,q 2 0 1 - q, 1 2 ́ 1 2, 4 2

(^03) 3 – √ 3 3 + √ 3
A-q, 3- 23 D ́C 3 + 23 ,qB
(^0153)
C0,^53 D
04
1 - q, 0 4 ́ 3 4,q 2
–1 – 12 0 13 1
A-q,-^12 D ́C^13 ,qB
3
2
3

-^02

C-^32 ,^32 D

3

2

3

-^015

A-q,-^32 D ́C^35 ,qB

031

1 - q, 1 4 ́ 3 3,q 2

–4 0 6

1 - 4, 6 2

–1 0 5

1 - q,- 12 ́ 1 5,q 2

5 - 2, 5 6 3 - 2, 5 4 1 - q,- 24 ́ 3 5,q 2

5 6 1 - q, 1 2 ́ 1 3,q 2 1 1, 3 2

A-^32 ,qB

01 5

051

R(x)

x

22,50020,000

15,000

10,000

5,000

(^0255075100)
(25, 22,500)
R(x) = (100 – x)(200 + 4x)
R 1 x 2 = 1100 - x 21200 + 4 x 2 = 20,000+ 200 x- 4 x^2
1 2
x^2
ft^2
29.vertex: axis: ;
domain:
range:
31.vertex:
axis: ; domain:
range:
–7 0
–2
y
x
5
x = 3y^2 + 12y + 5
1 - q,q 2
y=- 2 3 - 7,q 2 ;
1 - 7,- 22 ;
x
y
01
–4
5
x = –^15 y^2 + 2y – 4
1 - q,q 2
1 - q, 1 4 ;
1 1, 5 2 ; y= 5