Answer Key

Interval Notation

1. ( , 10] 2. ( ,3] 3. (6, ) 4. 1

,2

5. (2,5) 6. [ 12, 3] 7. ( 17,24]

8. [125,400) 9. ( , 0.40) ( 0.40, ) U 10. ( , 2) ( 2,2) (2, ) U U 11. ( , 4) [3, ) U 12. ( ,7] (10,12) U 13(a) [5, 7] (b) (5, 7) (c) 3 8x (d) ( ,9] (e) (4, ) (f) ( 4,7] (g) ( ,1) (h) [ 3, ) 14.(a)3 9x (b) 4 5x (c) 5x (d) 6x 15. (a) [0,6) (b) [ 7, ) (c) [5,8] (d) (7,10) (e) (5,8] (f) (2,9) (g){5} (h) (i) [ 2,10) (j) (4,10) 16. -3 Y N Y Y 17. (a) [3, ) ; (0,9) ; [2,6] ; [1, 4] [7,8]U

(b) (c) 3 4; [3, 4]x

N N N Y Y Y Y Y 7 N N Y Y

Interval Notation Worksheet

1. ( ,3] ; 2. 4x ; 3. 2 6; [2,6]x

4. 5x ; 5. 1; ( ,1]x 6. ( ,1) [5, ) U ; 7. 5 1; ( 5, 1)x 8. ( , ) ; 9. 1 or 2x x ; ( , 1] (2, ) U

10. 1 4x ; 11. (7, ) ; 12. 2 2x ;

Lesson 1.1 1. Commutative for Addition 2. Commutative for Multiplication 3. Identity for Addition 4. Distributive for Multiplication over Additon 5. Inverse for Multiplication 6. Associative for Multiplication 7. Distributive 8. Commutative for Addition 9. Associative for Addition 10. Inverse for Multiplication 11. Identity for Addition 12. 5 ( )a b c Given (3 )3b b Given

5( )ab ac Distributive 13 3b

b

Def. of Division

5 5ab ac Distributive 13 3b

b

Associative for Multiplication

13 3 b

b

Commutative for Multiplication

3 (3 1) Inverse for Multiplication 3 3 Identity for Multiplication = 9 Multiplication

Answer Key

14. 3 ( 4 2 )a a Given 15.

1 152 in 28 in 80 inches

4 4

16. 132 oz + 12 oz = 144 oz. 17. 2

1 miles3

18. 0.25 miles 60 sec 60 min

3.12 sec 1 min 1 hr

900 miles288.46

3.12 hour

3 (2 2 )a a Def Sqr. Rt. 3 (2 2 )a a Def of Subtraction 3 ( 2 2)a a Commutative for Add. (3 2 ) 2a a Associative for Add. 1 2a Addition

2a Identity for Mult

19. 5 days 8 rounds 3980ft 1mile

1 week 30.152 miles1 week 1 day 1 round 5280 ft 20. 5 pieces

21. Total = 6 min 38 sec; Average = 99.5 sec 22. 1800 mph 23. 5.682 mph

24. 31.25 drops per minute 25. yes; 3 3 3

3 w 3

kg 1000g 1 pound 2.54 cm 12 in lbs.001 62.372

cm 1 kg 454 grams 1 in 1 ft ft

26a. 21,195,743 burgers 26b. 87 years + present age 27. Answers vary 28. Answers vary 29. Commutative for Mult. 30. Associative for Mult. 31. Inverse for Mult. 32. Identity for Mult. and Distributive 33. Distributive 34. always; associative prop 35. always; associative prop. 36. sometimes; If a, b, and c are all 0 it works; else it doesn’t 37. sometimes; if a, b and c are all 1 it works 38. always; distributive prop. 39. sometimes; if a, b and c are 1 it works 40. 4.032 liters of first solution and 12.019 liters of second solution Lesson 1.2 1. 4x 2. 3 28 ( )a x y 3. 8( 6) 4. 16 5. 1 6. 4 7. 43 8. 3 / 23 9. 17 /12

10. 2,000,000 11. 20 4x 12. 2 15 6x x 13. 2 15x y 14. 2 22x xy y

15. 3 2 2x x y y x 16. 6x x 17. 2 2 1xy x y 18. 3 2 3 212 2

2x y x y y y

19. 255x 20. if p > 6, 340 + 35(p – 6) = 35p +130; 10 people = $480; 4 people = $340 21. if m > 300, 19.99 + .10(m – 300) + .25d ; Cost for m = 375 and d = 54 is $40.99 22a. 51x + 12y 22b. 50.4x + 15y 22c. purchase = $930; proceeds = $1029 23. 4ax2+7x b (bx2

ax + 3) = 3x2 + 9x 8

24. 3ax3 8bx2

(10x2 + 2ax

b) + 3x3

4ax = 12x3 18x2 18x;

25. (2ax + b)2 (abx2

6a) = 6x2 + 40x + 37

26. (7 + 3a) (2b ÷ 4)2 =74

27. 4a (ab + b) a2 = 15

28. ab 5b ((2b)2 + 4a) = 21

Lesson 1.3

1. 21x 2. 20

3x 3.

5

8x 4. no solution 5. 1x 6. 5x 7. 2x

8. 11

3x 9. ( , ) 10. 4x 11.

6

5x 12. 0x 13. 1x 14. 5x

Answer Key

15. ( , ) 16. 5x 17. 1x 18. 7

9x 19.

2

d rt

a 20.

2 2

( 1)

S and

n n

21. $106.21 22. 72 feet 23. 58 mph 24. 2.5 hrs 25. 6 hours 26. 9 minutes

27. 600

85.714 min7

28. 22 min and 38.491 sec 29. 8.7 feet 30. 25 31. 40 ,140

32. 34 and 56 33. 43, 45, 47, 49 34. 34, 36, 38, 40 35. 4 hours 36. 300 and 600 mph 37. 3.5 and 15.5 38. 18, 18, 29 39. 20 miles 40. 76 yds by 236 yds 41. 3 pm 42. $3000 43. 119 Section 1.4

1. 6 3

2

xy

x

2.

3 3

4 2y x 3.

1

2y 4.

16 6

2

xy

x

5.

14 12

15

xy

6. 20 35

3 5

xy

x

7.

932

5F C 8. 1 2

2Ab b

h 9.

3Vr

h 10.

SR r

s

11. 2

4 3

xyz

xy x y

12.

1

xy

x

13.

xyz

xy y x

14.

5

3 4

z xy

xz

15. peanut=$2.00;

caramel = $1.50 16. 2 1.5P b c ; P = profit; b = # of peanut; c = # of caramel

17. 130 peanut bars, 260 caramel bars 18. 2 32

3V r h r 19.

3

2

3 2

3

V rh

r

20. 8 ft

22. 2 22

VR

r

Literal Equations

1. 2

( )4

CA C

2.

2 3( )

4

sA s 3.

23 23

2

9( ) 4 36

16

VS V V

4.

3

( )48

hV h

5. 33 (5 )

( ) 1525

hV h

6. 5 5 5( ) 3 (1 3)V x x x x 7.

2

S PhB

8. 21

2A b hb

h

9.

22

2

S rh

r

10.

932

5F C 11. 1

21 1

RR

RR

12.

3

2

3

3

V hr

h

13. S

r Rs

14. L a d

nd

15. 1t

Tr

P 16.

y bm

x

17. 1 1( )y m x x y

18. 0 0ff

v v att

a

19.

1

2

dr dA

dt r dt ;

in2

min

dr

dt 20. 23

( )4

A s s 21. 33( )

24V s s

22. 31( )

4V s s 23. 24 ft 25. 15 ft 26. 20 ft 28. 24 ft 29. 7 ft 31. ( ) 7 2b t t

32. 2( ) 625h b b 33. 2( ) 625 (7 2 )h t t 34. no; h(t) is not a linear function

Section 1.5 1. 8 18y x 2. 7 89y x 3. 2 28y x 4. 0.6 4y x 5. 0.5 0.75y x

Answer Key

6. 0.7 7.2y x 7. 24 = 7.50 +0.75s; 22 songs 8. 14.25 mph 9. $525,300 10. 5 painters 11. 6 feet 12. 4.75 inches 13. minimum amt = $1.59; total = $7.95 14. 6 quarters 15. 6 inches 16. 2 feet and 3 inches Section 1.6

1. 1

,2

2. ( 5, 3] 3. ( ,3] [7, ) 4. ( ,0) 5. ( , 4) 6. ( ,3.5]

7. ( ,3) (3.5, ) 8. [2,3] 9. 32

,7

10. 11. 12. ( , )

13. 5

or 28

x x x

14. 3.1 or 4x x x 15. 40 100x x 16. 14

233

x x

17. 1,108,451 1,211,537P 18. $10 shirts = 0, 1, 2 and $7 shirts = 6, 5, 4 19. 5 frames and 10 candles or 6 frames and 9 candles or 7 frames and 8 candles

20. 2 2

50 , 85 , 633 3

x y z 21. 5 paint kits and 10 brush kits or 6 paint kits and 9 brush

kits or 7 paint kits and 8 brush kits or 8 paint kits and 7 brush kits or 9 paint kits and 6 brush kits

or 10 paint kits and 5 brush kits or 11 paint kits and 4 brush kits. 22. 2 92

3 3x

23. 63 21 105 35

;8 2 8 2

x y 24. 20 stamps at 22 cents 25. 6, 12, 10

26. Daphne = 4, Jeanine = 4, Greg = 8, Suzanne = 1 27. 98x 28. 37n Section 1.7 1. 1 or -5 2. 0 or 6 3. 2/5 or 8/5 4. 5 or 1x x 5. -1 or 9 6. 7. 7/8 or 25/8 8. 9. 9/4 10. 20 4x 11. 8/5 or 28 12. 6 or 1x x 13. 10 / 9 6x 14. 1.7x 15. 2 3x 16. -1.5 or -0.75 15. x a b 16. x ab

17. 2 or 0x a x 18. c b c b

xa a

19.

c b c bx

a a

20. or c b c b

x xa a

21. or

c b c bx x

a a

22. 0.365 0.01d

23. 238,850 13,150d 24. 9.75 0.375w 25. 8 4d

26. 3.85 0.35; 1.2 0.1;c t 5.05 0.45w

27a. 238.095 263.158x 27b. 90 0.05x x 27c. 85.714 94.737x

Answer Key

Functions the Beginning 1. D:{0, 1, 2, 3, 4}, R: {1, 2, 3, 4}, is a function, is not one-to-one 2. :{ 2, 1,0,1}, :{ 3, 1,1,3,5}D R , not a function 3. : ( , ), : ( ,0]D R , is a function, not one-to-one 4. :[0, ), : ( , )D R , is not function 5. :{ 2, 1,0,1,2}, :{ 2, 1,1}D R ,not a function 6. :{ 2, 1,0,2,4}, :{1}D R , is a function, is not one-to-one 7. :{0,1,2,5}, :{ 3,0,2,4}D R , not a function 8. :[ 7,8], :[ 4,5]D R ,is a function, not a one-to-one 9. function 10. function 11. not a function 12. function 13. function 14. not a function 15. not a function 16. function 17. not a function 18. not a function 19. function 20. function 21. ( ,3) (3, ) 22. ( , 1) ( 1, ) 23. ( , 3) ( 3,3) (3, ) 24. ( , ) 25. ( , 4) (4,7) (7, ) 26. ( , 10) ( 10,2) (2, ) 27. [5, ) 28. ( , ) 29. [ 7, ) 30. ( , 4) ( 4,1.5] 31. (2.5, ) 32. ( , 4) (6, )

33. 7 2 2

, ,3 3 3

34. ( , 2) (7, ) 35. [4.5, )

Real World Functions – Student answer will vary. Function Value and Functions Notation

1. 6 2. 2 4x 3. 2 4 4. 10

2

x 5. 24 6. 23 18 22n n 7. 23 18 22n n 8. –9

9. 9 10. 2 11. 1 12. 0.5 13. 9.5 14. 5 15. 0.5 16. 2 6 6h h 17. 2 18. 6 3x h 19. 20. always true 21. not always true

22. always true 23. not always true Function Behaviors and Characteristics 1a. 6 b. doesn’t exist c. positive d. negative e. –2 f. (–3, 2) g. (–3, 4] h. ( 2,3) (4,6] i. 1 and 1 j. 2 k. 5.5 l. once m. once n. 4 o. none p. 6 q. ( 3, 1) and [1,4] 2a. 0; 3 b. 5.1 c. 2.9 and 2.6 d. 12.1 and 1.6 e. ( 2.9,0.3) and (2.6, ) f. ( , 2.9) and (0.3,2.6) g. ( 4, 1) and (2,3) h. 4, 1,2,3 i. 12.1 j. 3a. [0,6) and (16,18]; function is positive b. (6, 16); function is negative c. at 6 and at 16 di. 60 m dii. 105 m diii. 15 m div. 180 m e. – 30 f. (6, 10); (16, 18) g. (2, 6); (14, 16) 4a. ( ,6) b. ( ,5] c. 2 d. ( 2) 0.5, (0) 5, (2) 1, (4) 1,g g g g

(6) doesn't existg e. ( 2)g f. ( ,0), (2,6) g. (0, 2) h. 2 i. 5 j. ( , 2.25), [2,3)

Answer Key

Characteristics of Functions 1. a) ( , ) b) ( , 4] c) -2; 2 d) 4 e) (-2,2) f) ( , 2);(2, ) g) ( ,0) h) (0, ) i) none 2. a) ( , ) b) [0, ) c) -3; 3 d) 3 e) ( , 3);( 3,3);(3, ) f) none g) ( 3,0);(3, ) h) ( , 3);(0,3) i) none 3. a) [ 8,8] b) [ 6, 2] c) -2; 4 d) 2 e) (-2,4) f) ( 8, 2);(4,8] g) ( 8,0) h) (3,6) i) (0,3); (6,8) 4. a) [ 3,3) b) ( 4,2] c) -3; 1/3 d) about ½ e) (-3, 1/3) f) (1/ 3,3) g) ( 3, 1) h) ( 1,3) i) none 5. a) [ 7,3] b) [ 4, 4] c) -3; 5/3 d) 5/2 e) (-3, 5/3) f) [ 7,3);(5 / 3,3] g) ( 7, 1) h) ( 1,3) i) none 6. a) [ 7,5] b) [ 5,4] c) -7; 2 d) 4 e) (-7, 2) f) (2,5] g) ( 7, 4);( 1,0) h) (0,5 / 2);(4,5) i) (-4, -1); (5/2, 4) 8. a) [ 7,5] b) [ 3,6] c) 5.25, 4.25 d) 6 e) ( 5.25,4.25) f) [ 7, 5.25);(4.25,5] g) ( 7, 3) h) (3,5) i) (-3, 3) 9. a) [ 3,3] b) [ 2,2] c)-3; 0; 3 d) 0 e) (-3, 0) f) (0, 3) g) ( 3, 1.5);(1.5,3) h) ( 1.5,1.5) i) none Even and Odd Functions 1. Fig. 1 and Fig. 2 2. Fig. 9 3. Even 4. Odd 5. Neither 6. Neither 7. Odd 8. Even 9. Odd 10. Neither 11. Even 12. Odd 13. Odd 14. Answer vary. Some possible answer are: Polynomials have all even or all odd exponents on the variables. 15. Odd; Neither; Even 16. No 17. If ( )f x and ( )g x are both odd, then ( ) ( )f x f x and ( ) ( )g x g x . Therefore, ( ) ( ) ( ) ( )f x g x f x g x so the resulting function is even. If ( )f x and ( )g x are both even, then ( ) ( )f x f x and ( ) ( )g x g x . Therefore, ( ) ( ) ( ) ( )f x g x f x g x so the resulting function is even. 18. If ( )f x is odd and ( )g x is even, then ( ) ( )f x f x and ( ) ( )g x g x . Therefore, ( ) ( ) [ ( ) ( )]f x g x f x g x so the resulting function is odd. Transformations of Graphed Function 1. 2. 3. 4.

Answer Key

5. 6. 7. 8.

9. 10. 11.

12. right 2 13. up 2 14. vertical stretch 2, down 1 15. horizontal compression ½, down 3 12. 13. 14. 15.

16. vertical compression ½ 17. left 1, down 2 18. flip over the x-axis 16. 17. 18.

19. verical stretch 2, flip over the x-axis, right 1, up 2 20. vertical compression ½, flip over the y-axis, down 3

Answer Key

19. 20. 21. flip negative part of function over the x-axis 22. flip negative part of function over the x-axis, down 2 23. right 1 and down 2, flip negative part of resulting function over the x-axis 21. 22. 23.

Graphical Transformations 1a. D: [0, 20], R: [0, 14] b. 14; 8 c. 20; 8 d. 3/4 e. 171 square units 2a. D: [0, 20], R:[2, 9] b. 9; 8 c. none; 6 d. 3/8 e. 125.5 square units 3a. D: [2, 22], R: [0, 7] b. 7; 10 c. 22; none d. -7/12 e. 85.5 square units 4a. D: [0, 20], R: [-7, 0] b. 0; 20 c. -7; 8 d. 85.5 square units e. [8, 20] 5a. D:[3, 23], R:[5, 26] b. 26; 11 c. 5; 23 d. none; none e. 356.5 square units f. [11, 23] 6. change: y-intercept, range, maximum value, area unchanged: domain, x-int, x of maximum 7. change: domain x-intercept, x of maximum unchanged: maximum value, area need more info to determine: y-intercept, area Transformation of Points without a Graph 1a.(2, 6) 1b. (2, 4) 1c. (2, -3) 1d. (2/3, 3) 1e. (-2, 3) 1f. (3, 3) 1g. (0, 3) 1h. (2, 0) 1i. (4, -1) 1j. (0, -4) 1k. (4, 14) 2a. f(x – 1) or f(2x) 2b. f(x – 5) + 1 2c. f(0.5x) or f(x + 2) 3. Amount of money Molly will earn from Thursday of one week to Friday of the next week 4. 5. 6. 7. 8. 9. x y x y x y x y x y x y -7 -5 -6 -4 -3.5 2 -5 6 -7 6 -5 11 -4 -9 -3 -12 -2 -2 -2 8 -4 18 -2 27 -2 -18 -1 -30 -1 -11 0 12.5 -2 45 0 63 -1 -10 0 -14 -0.5 -3 1 8.5 -1 21 1 31 2 -4 3 -2 1 3 4 5.5 2 3 4 7 3 -1 4 4 1.5 6 5 4 3 6 5 -5 5 0 6 6 2.5 7 7 3.5 5 9 7 -9 6 5 7 16 3 12 8 1 6 24 8 -2910. x y 11. (0.5 )f x 12. ( 1)f x 7 0 4 -4 13. ( )f x 14. 3 ( 4)f x

Answer Key

2 -13 1 -5 15. 0.5 (4 )f x -2 1 -3 4 16. 2 ( 1) 3f x -5 5 -6 10 Functions Transformations 1. O 2. D 3. K 4. B 5. G 6. M 7. F 8. J 9. A 10. H 11. C 12. I 13. N 14. L 15. E Transformations of Parent Functions 1a. cubic b. left 1, down 2 c. 3( 1) 3y x d. D: ( , ) ; R: ( , )

2a. quadratic b. right 1, up 2 c. 2( 1) 2y x d. D: ( , ) ; R: [2, )

3a. square root b. flip over x-axis, right 2, up 1 c. 2 1y x d. D:[2, ) ; R: ( ,1]

4a. absolute value b. vertical stretch 2, right 2 c. 2 2y x d. D: ( , ) ; R: [0, )

5a. absolute value b.flip over x-axis, right 2, up 3 c. 2 3y x d. D: ( , ) ; R: ( ,3]

6a. square root b.vertical stretch 3/2, left 1, down 2 c. 3

1 22

y x d. D:[ 1, ) ; R: [ 2, )

7a.quadratic b.flip over x-axis, vertical stretch 2, left 3, up 4 c. 22( 3) 4y x d. D: ( , ) ; R: ( , 4]

8a. rational b. left 2, down 4 c. 1

42

yx

d. D: ( , 2) ( 2, ) U ; R: ( , 4) ( 4, ) U

9a. quadratic b. flip over x-axis, vertical stretch 3 c. 23y x d. D: ( , ) ; R: ( ,0] 10a. greatest integer b. vertical stretch 2, down 1 c. [ ] 1y x d. D: ( , ) ; R: {odd integers} 11. right 3, down 2 12. flip over x-axis, vertical stretch by 2 13. flip over x-axis, horizontal compression by 0.5, up 1 14. vertical compression by 0.5, left 3 15. flip over x-axis, vertical compression by 1/3, horizontal compression by 1/2, right 5/2, up 1 16. vertical stretch by 4, horizontal compression by 1/2, left 3/2, down 2 17. vertical stretch by 2, left 4, up 1 18. right 1, down 2 19. left 2, down 1 20. vertical stretch by 2, horizontal stretch by 2, left 6, up 1 21. vertical stretch by 1.5, left 1, up 4 Review 1. a) 2y x b) flip over x-axis, vertical stretch by 2, up 4 c) 22 4y x d) D: ( , ) ; R: ( , 4]

2. a) 2y x b) right 1, down 4 c) 2( 1) 4y x d) D: ( , ) ; R: [ 4, )

3. a) 3y x b) vertical compression ½, up 1 c) 311

2y x d) D: ( , ) ; R: ( , )

4. a) y x b) flip over x-axis, right 5, up 6 c) 5 6y x d) D: ( , ) ; R: ( ,6]

5. a) y x b) vertical stretch by 2, right 5, up 2 c) 2 5 2y x d) D: ( , ) ; R: [2, )

6. a) y x b) flip over x-axis, vertical stretch 4,up 2 c) 4 2y x

Answer Key

d) D: [0, ) ; R: ( , 2]

7. a) 1

yx

b) right 3, up 2 c) 1

23

yx

d) D: ( ,3) (3, ) ; R: ( , 2) (2, )

8. a) 1

yx

b) vertical stretch 3, right 1, up 2 c) 3

21

yx

d) D: ( ,1) (1, ) ; R: ( , 2) (2, ) 9. quadratic parent; vertical stretch 2/3, right 5, down 1 10. square root parent; vertical stretch by 3, right 1, down 4 11. cubic parent; flip over x-axis, vertical stretch of 2, right 1 12. absolute value parent; flip over the x-axis, right 2, up 4 13. quadratic parent; vertical stretch by 1/3, left 6, up 2 14. absolute value parent; vertical stretch of 4/3, right 2, up 7 15. square root parent, right 4, down 2 16. rational parent; vertical stretch 3, left 2, up 4 17. exponential (power of 3) parent; flip over x-axis, right 1, down 4 18. 2( 3) 5y x

19. 3 5y x 20. 1

2 32

y x 21. 2sin( 2.5) 1y (1st set of #22 – 27 are graphs)

22. 23. 24. 25.

26. 27.

22. -3 23. 1 – 2n 24. -32 25. 23 24 44x x 26. 6 312 12 1x x 27. 8 28. 8 29. 2 6x x 30. 12 12x 31. 6 6x 32. -2 33. 6 3x h 34. 5.5a 35. 1n 36. ( 1) 4f x 37. ( 1)f x 38. (4 ) 5f x 39. function 40. not a function 41. function 42. not a function 43. ( , 5) ( 5,5) (5, ) 44. ( ,6) (6,7) (7, ) 45. [4.5, ) 46. ( , ) 47. [ 4, 1) (5, ) 48. ( , 3] [13, ) 49 and 50. answers may vary 51a. [ 4,6) b. [ 3,6] c. 2 and 4 d. 3 e. ( 2, 4) f. [ 4, 2); (4,6) g. ( 4,0), (1,3), (5,6) h. (0,1), (3,5) i. none j. 0 and 3 k. 3 and 6 l. 1 and 5 m. 2 and 2 n. 6 o. 3 52. even 53. odd 54. odd 55. neither

Answer Key

Section 2.2 1. they are equal 2. their product is -1 3. vertical lines 4. horizontal lines 5. -11/4, falls 6. 65/92, rises 7. 3/4, rises 8. 0, horizontal 9. -3/4, falls 10. undefined, vertical 11. line 1 is steeper 12. line 2 is steeper 13. k = 6 14. k = 4 15. k = 44 16. k = -1/9 17. yes, slopes are equal 18. no, slopes are not equal 19. pillar = 1000/21; pyramid = 55/17 20. 3 deg/hr; 73o 21. 225 mph 22. Since these lines are parallel, we know the slopes are equal. If the slopes are equal, then the y-intercepts must be different for the lines to be distinct.

23a. 1 gal hr

9 hr b.

1 gal hr

120 hr c.

gal hr0

hr 24a.

ft52

sec b.

ft44

sec c.

ft84

sec d.

ft52

sec

25a. 8.4 b. 8.04 c. 8.004 26. m

8sec

27. 4 28. 29a. -6 b. 0 c. 4 d. 2 e. 2

30. (0.5, 1.5) 31. 2 32. a.-3/2 b.-3/2 c.-3/2 d.-3/2 34.(1, 3.75) 35.-3/2 Section 2.3 1. m=-1/2, y-int=2, x-int=4 2. m=-2/3, y-int=2, x-int=-3 3. m=0, y-int=-3, x-int=none 4. m=2, y-int=-5, x-int=5/2 5. . m=-4, y-int=-3, x-int=-3/4 6. m=3/4, y-int=-3, x-int=4 7. m=undefined, y-int=none, x-int=6 8. . m=5/4, y-int=-2, x-int=8/5 9. k = -3 10. k = -5/3 11. k = 2 12. k=19/84 13a. V-int = 500,000, t-int = 6, t-int is the time when the value is $0 b. slope = -250,000/3 $/yr; slope represents the $ value the equipment drops each year 15a. 4.5x + 10y = 2500 b. (0, 250), (20, 241), (100, 105), (200, 160)

16a. b = 100 – 6.25w ; b = 175 – 12.50w b. Your brother; his x-intercept is smaller c. find the x-intercept of each by substituting 0 for y d. yes, now you pay off earlier 17. False, A = -7, B = 4, slope = 7/4 18. True, slope = 0 have one y-intercept, undefined slope have one x-intercept and all other slopes have an x-intercept and a y-intercept. 19. False; x = 4 Section 2.4 1. y – 6 = 2(x – 7) 2. x = 3 3. y + 2 = 3/8(x – 7) 4. y = 9 5. y + 3 = -1/3(x – 2) 6. y + 3 = 1/5(x + 1) 7. y – 3 = -3(x – 5) 8. x = 5 9. y + 2 = -(x + 6) 10. y = 1 11. y – 10 = 2/3(x – 8) 12. 5x + y = 7 13. 2x + 3y = 20 14. 8x – y = 1 15. y = 2.5x + 12.5 16a. p = 2,839,974.1t + 152,271,417 b. yes within 5% of forecasted c. no, not within 5% 17a. about 4 b. h + 4; 5, 3, 4.1 c. 4 b/c the slope is approaching 4 as h approaches 0.

Answer Key

18. y = 2x + 0.5 19. 6x +4y = 21 20. y – 66 = 50(x – 4) 21. y – 66 = (-1/50)(x – 4) 22. y = -4x + 1.5 23. -2/27 24. S(0, 1/3) 25. R(9/2, 0) 26. 2 27 9x y 27. 0.75 units2 28. -1/4 29. 4 3x y 30. 9/8 units2 Linear Models 1a. 72 21C q b. $8.85 c. Pint matches, quart is higher d. 4.5 quarts e. cost of carton f. cents/quart, the price of the milk itself 2a. 4 160C t b. 200 chirps per minute

c. 70 F d. 40 F ; temp when a cricket stops chirping e. D: [40, 120]

f. nothing, you cannot have a negative chirping rate 3a. 3 22s l b. Size 14 c. 44

inches3

4a. there is constant rate of change; cal30 degree ; 30 3630C t b. 2130 calories/day

c. 5130 calories/day d. 121 C ; no b/c water boils at 100 C 5a. constant rate of change b. 60 4500d t c. 75 sect d. 4500 m e. you weren’t always at constant velocity f. 216 km/hr 6a. 7 90y x b. 139 mph c. 1 uphill because it is positive d. 90 mph max speed on 0 hill e. 12.857 ; steepness at which the car can no longer move

7a. 5

4553

V t b. 555 cm3 c vary d. 955 cm3 e. 273 C ; absolute zero

8a. the equation is in the form y mx b b. 615 ft c. 17 stories d. # of feet in each story e. 35; it represents the extra cable needed f. {2, 3, …largest number of stories possible} 9a. 0.33 4478.50t i b. $9761; $25,076.30 10. C = 1.25d + 2.50; $127.50 Circles and Tangents and Secants (Fix and error in #5 and 6, x + 1 should be x – 1)

1. 2. 4/3 3. -3/4 4. 3

4 ( 3)4

y x 5. no 6. 4 and -3

7. P(4, 3) and Q(-3, -4) 8. 3/4 9. -4/3 10. 4 25

3 3y x 11. -3/4 12.

3 25

4 4y x

13. no, because the line PQ does not pass through the center of the circle 14.(6, 14) 15. -5/12

16. 5

14 ( 6)12

y x 17. (39.6, 0) 18. 19. (-4, -10)

Answer Key

20. (-11, 7) and (13, -3) 21.(1, -2) 22. 2 2( 1) ( 2) 52x y 23. 3

2 ( 7)2

y x

24. 3

6 ( 5)2

y x 25. parallel 26. -3/2

Section 2.5

1. yes; 5k 2. yes; k=8 3. yes; k=1.5 4. no 5. no 6. yes; k=4 7. no 8. yes, y = x/15

9. yes 10. yes 11. yes 12.1

3y x ;

5

3y 13.

15

4y x ;

25

4y 14. 0.4y x ; 2y

15. no, because there is a fixed fee 16. yes, the constant of variation is p 17a. 5

8m k

b. yes you are speeding; 100 kph = 62.5 mph 18. 21

2y x ;

9

8y 19. 33.2y x ; 0.2048y

20. 48

27y x ; 31,104y 21. it will be 4 times as large 22. (0, 0)

Direct Variation Word Problems 1a. c = 0.7p 1b. 35 cups 1c. 17 people 2a. p=2.2k 2b. 220 lb; 55 lb; 330 lb 2c. 75 kg 2d. # of kg in a lb 3a. p=0.43d 3b. 21.5 psi 3c. 151.163 ft 4a. r=(65/32)n 4b. $2.03 4c. 4923 cans 4d. cents per can refund 5a. t = 3d 5b. seconds per kilometer (it is the reciprocal of the speed of sound) 5c. 3 sec; 7.5 sec; 30 sec 5d. 9.67 km 6a. V = 0.025T 6b. 10; 15; 22.5; 30 6c. at too high a temp balloon might melt; at too high a volume balloon might burst; too low a temp balloon might become brittle and the air might liquefy Section 2.6 1. Answers vary; about y = 4.05x – 3.3 2. Answers vary; about y = -1.125x + 2.3125 3a. negative b. y = -0.241x + 290.989 c. no; b/c the points lie in a curve not a line 4b. P(t) = 0.33t +15.63 c. P(18) = 21.57 million people d. 0.33 million people per year e. P(-15) = 10.68 million people f. population is growing at a rate of 330,000 people per year g. during the year 2062 5b. C(H) = 0.373H + 7.327 c. circumference inches/height inches d. 17.035 inches e. 27.005 inches 8. 153.59 9. Given line not fit data well; linear reg line from calculator is y = -1.098x + 39.161; square differences = 7.189; linear reg line is better fit Piecewise Functions

1a. [-5, 4] b. [-2.5, 2] c. (-5, -2) d. (1, 4) e. (-2, 1) f.

15 2

22 2 1

4 101 4

3 3

x x

y x

x x

Answer Key

2.

2( 2) 3 5 0

11 0 4

22 11 4 7

x x

y x x

x x

3a. 3

5 022 0

x xy

x x

b. 3

02

2 0

x xy

x x

or

35 0

22 5 0

x xy

x x

4a.

3 0 1

2 71 4

3 3( )5 4 7

5 207 10

3 3

t t

t td t

t

x t

c.

3 0 1

21 4

3( )0 4 7

57 10

3

t

ts t

t

t

5.0

0

x xy

x x

6.2 5 3

2 7 0

x xy

x x

7a. 0.6 in/hr b. 0.64 in/hr c. 0 in/hr d. 1 in/hr

8. yes,(-2, 0), (0, 3), (2, -1) 9.

9a. ( , 1) ; [ 1, ) b. D: ( , ) ; R: ( ,1] c. -8 d. -21 e. 8

2.5 and3

10a. k = 5 b. m = 7/6 11. a = 2 12.a = -2 13a.

50 0 3

( ) 150 3 6

60( 6) 0 3

t t

d t t

t t

b. c. 115 miles d. 8 hours 52 minutes

14. 3

3 5 4

2 1 4 2

2( 3) 2 4

x

y x x

x x

15.

3

2

2( 5) 4 6 4

1 4 1

( 2) 4 1 5

x x

y x

x x

Answer Key

Section 2.7 1. True; because ( ) 2f x x is even so ( ) ( )f x f x 2. False; order of process described is

wrong, need to flip first 3. True; moved f(x) left 2 and down 1 4. True; because 2 is positive 5a.D:[-4, 5]; R:[-3, 4] c.flip over x-axis, vertical stretch 3, left 3, down 3 d.D:[-7, 2]; R:[-15, 6] 6a. D: [-8, 8]; R: [-7, 5] c.flip over x-axis, vertical compression. by ½, right 6, up 5

d. D: [-2, 14]; R: [2.5, 8.5] 5b. 6b.

7. 8. Section 2.8 1. dashed line through points (2, 4) and (-2, -3) shading below the line 2. dashed line through (-2, 1) and (2, 3) and shading below the line 3. solid absolute value graph with vertex at (2, 1) , opening up with a slope of 2 , shaded inside 4. dashed absolute value graph with vertex at (-2, 1.5) opening down with slope ½, shaded above 5. solid absolute value graph with vertex at (3, 3) opening down with slope 3, shaded below

6. 2

13

y x 7. 3 3

4 2y x 8.

12 4

2y x 9.

1 10

3 3y x 10 4 12y x

11. 2 37

5 5y x 12. 2 3y x 13a. 3 2 88m f 13b. line with m-intercept of 88/3

and f-intercept of 44 13c. no, the score would have been 89 and the highest score was 88.

Answer Key

Sections 3.1 and 3.2

1. (3, 1) 2. (-2, -1) 3. (1, -4) 4. 5

,32

5. 4 13

,5 5

6. no solution

7. infinitely many solutions 8. 2 8

,5 5

9. 16 7

,5 5

10. two lines with the same slope

and different y-intercepts 11. the same line written in two different ways 12. two lines with two different slopes 13. a = 2, b = 3 14a. p = 50, quantity = 2,100 b. 50 190p 15. 3, 4x y 16. $5,000 at 6.5%, $15,000 at 8.5% 17a. demand increases and supply decreases b. at $21.50, the supply and demand quantity will be 135,000 Section 3.3 1. 2. 3. 4.

5a.

15 12 300

10 18 250

15 16 350

x y

x y

x y

b. x = 21, y = 3

Section 3.4 1. (2, 1, -3) 2. (3, -0.5, 2) 3. (1, -4, 2) 4. (1.5, -2, -1) 5. no solution 6. (1/3, -2/3, 1/3) 7. (4, -2, -5) 8. (7, -21, 18) 9. (0.5, 1, -1.5) 10. line x + y = 2 11. (8/15, -1/8, -4/11) 12. a = 1/2, b = -2, c = 0 so the quadratic equation is 20.5 2y x x Systems of Equations

1. 3 10 48

; 6, 37 4 54

b sb s

b s

2. 4 8 52

; 5, 43 2 23

c tc t

c t

3. 100 70

; 30, 0.404 46

f mf m

f m

4. 5( ) 800

; 130, 308( ) 800

p wp w

p w

5. 1.5( ) 6

; 3.75, 0.251.5( ) 5.25

f cf c

f c

6. 12

; 3, 9 number = 3910 15 2(10 )

t ut u

u t t u

Answer Key

7.

20000;

1.5(0.08 ) 1.5(.06 ) 2160

$12,000 8%, $8,000 6%

x y

x y

at at

8.

2 1.00

5 5 3.75 ;

2 2 2.50

0.50, 0.25, 0.75

c b

c b

b p

b c p

9.

12

2 3 16 ; 2, 4, 6

3 2 24

a p s

a p a p s

p s

10.

18

3 5 17 ; 7, 9, 2 number = 792

2 4 22

h t u

t u h t u

h u

11.

10000 $4,000 at 5%

5 6 7 61000 $1,000 at 6%

3000 $5,000 at 7%

x y z

x y z

x y

12.

10

.10 .30 (.15)(10)

7.5L of 10%, 2.5L of 30%

x y

x y

Geometry Review

a) 1

13

y x b) 3 19y x c) (6, -1) d) 40 2 10 e) 90 3 10 f) 30 units2

g) orthocenter is at (7, 2) Section 3.5 and 3.6

1.

42 9 20

7 11 2

42 30 16

2.

54 22

16 102

1 16

3. 116

120396 56

4. 13 17 29

21 28 0

5. x = -3, y = 6 6. x = -2, y = 0 7. yes, 2x2 8. no 9. yes, 2x3 10. yes, 2x3

11. 4 8

2 3

12.

4 7

1 0.5

3 6.5

13.

1 21

2 6

2 22

14.

2 3

35 14

13 18

15.

14 35

8 2

8 30

. 16.

35 17

30 22

5 1

17. x = 3, y = 4 18. x = -3, y = -1 19. yes 20. no 21. no 22. yes 23. A = 1,052 votes,B = 1,098 votes Section 3.7 1. 22 2. -10 3. -14 4. 9 5. 9.375 6. x = 7, y = -8 7. x = -7, y = 3, z = 9

8.

aw by az bz a b w x

cw dy cx dz c d y z

adwz bcxy bcwz adxy

9. if collinear then 1 1

2 2

3 3

1

1 0

1

x y

x y

x y

9a.

2 2 1

1 4 1 0

5 12 1

; points collinear 9b.

3 8 1

4 1 1 7

2 4 1

; points not collinear

10a. det A = 14, det B =-14 ; opposites 10b. det A = -43, det B = 43; opposites 11. both determinants are 0; If one column of a matrix is all zeros, its determinant is 0. 12. both determinants are 0; If two rows in a matrix are the same, the determinant is 0.

Answer Key

Section 3.8

1.

5 3

2 21

12

2.

1 1 1

10 2 51 1 1

20 4 103 1

15 5

3.

1 7 5

16 16 83 11 9

16 16 81 1 3

8 8 4

4. 27 34 8

9.5 12 3

5.

1

57

13

10

6.

11 7

1910 10

21 2 2

15 5

1; 1

2x y

7.

13 1 2 3 6

2 2 3 14 7

5 1 3 25 4

6, 7, 4x y z

8. n = 9/4 9. k = 4 10.

2 3 16

4 2 2

3 2 1

x y z

x z

y z

11a.

6 3 2 62

17

0

2 0

t f s e

t f s e

e f t

f s

11b.

6 3 2 1 62

1 1 1 1 17

1 1 0 1 0

0 1 2 0 0

t

f

s

e

11c. t = 8, f = 2, s = 1, e = 6

Answer Key

Factoring 1. (c – 2d)(c+2d) 2. (4a – 3b)(4a +3b) 3. not factorable 4. 9(x – 2)(x + 2)

5. 2(3a-2b)(3a + 2b) 6. 1

(3 1)(3 1)9

x x 7. 2( 2)( 2 4)c c c

8. 2 2(10 3 )(100 30 9 )f g f fg g 9. 2 4 2( 2)( 2 4)c c c 10. 3 4 3 4( 8 )( 8 )y z y z

11. 3 3(10 9 )(10 9 )t t 12. 4 2 8 4 2 4(11 12 )(121 132 144 )x y x x y y 13. ( 2 )( 2 )a b d a b d

14. 2( 9)u 15. 2(3 8)x 16. 2(5 4 )x y 17. 20.01(2 3)c 18. ( 2)( 3)x x 19. ( 9)( 3)t t 20. ( 8)( 2)x x 21. ( 11)( 4)f f 22. ( 1)( 6)x x 23. not factorable 24. (3 5)( 4)y y 25. (4 3)(7 2)a a 26. (7 2 )(2 )x y x y

27. (7 8)(7 9)mn mn 28. not factorable 29. (3 4 )(2 )ab c ab c 30. 23(2 3)w

31. 3( 9)( 1)x x 32. ( 4)( 1)k k 33. 2( 2)( 2 4)x x x 34. 2 (3 5)(3 1)b m m

35. 4 2 2( 4)( 2)( 2)v v v 36. 2 2( 3) ( 3)x x 37. 22 ( 10)( 10 100)p p p p

38. 1

( 2)( 1)3

x x x 39. 0.3(3 7)(2 5)x x 40. ( )( )x a x b 41. (2 3 )( 2 )s t m n

42. ( )( )f g f g m 43. 2 2( )( )a b a ab b a b 44. ( 1)( 2)( 2)x x x

45. ( )( )a b a bx y x y 46. ( 7)( 4)n nx x 47. 4 4(2 5 )(2 5 )a b c a b cx y z x y z

48. 2 2(8 5)(3 4)n nx x 49. 2 5 3 2 5 3(6 5 )(7 3 )a a a ax y x y 50. 2 2 2 26( 3 )( 3 )a b a bx y x y Section 4.1 and 4.2

1. y-int = 5, x-int = 4 6

2

, axis of symmetry: x = 2, vertex: (2, -3), Domain: ( , ) ; Range:

[ 3, ) , 22( 2) 3y x 2. y-int: 16, x-int: 2 8

and3 3

, axis of symmetry: x = -1, vertex: (-1,

25), Domain: ( , ) , Range: ( , 25] , 29 18 16y x x

Graph 1 Graph 2

3. 22( ) ( 2) 1

3f x x , no x-intercepts 4. 2( 1)( 4)y x x 5. 22( 1) 8y x

6a. 2(400 2 ) 2 400A x x x x b.(0, 200) c. 100 m d. 20,000 m2 7a. 400 ft b. 2.5 sec c. 0 ft/sec d. at 7.5 sec e. 32 ft/sec 8a. (0.45 0.05 )(36 2 )R x x 8b. x = 4.5 is max

9a. 200 2x

d

b. 200 2 2

( 100)x

A x x x

c.

10050, 31.831x d

Answer Key

10. 8 16 3 96

3.749333

32

x

Section 4.3, 4.4 and 4.5 1. x = 5 or -2 2. x = 1 or -1 3. x = -3/4 or 5/7 4. x = 7/5 or 2/3 5. x = 3, -3 or -2

6. x = 3/2, 6 or -6 7. x = -3 or 1 8. x = 10 or -1 9. x = 12 or 1 10. x = 3

11. x = 5

19

12. x = 2 2

9 2 13.

62

3 14.

423

6 15. 17 16. 0 or -15

17. 1 or 12 18. -1 or -7 19. 4/3 or -2 20. -3/2 or 3 21. 48 21 22. 12 42 23. 5 70

42

24. 1

3 25.

55

3 26.

6 3

4

27.

29 11 7

3

28.

12 3 2 8 3 2 6

3

29. a > -5

30. a < 0 31. 3.092 ft 32. w = 100 yds; area = 10,000 yd2 33. x = 5 34. 5.601; 2.800b h Quadratic Models

1. 2

6

9 3 26 3 2 5

4 2 21

a b c

a b c y x x

a b c

2. 2

4 2 41

9 3 72 4 11 3

25 5 48

a b c

a b c y x x

a b c

3. 2

16 4 7.3

36 6 12.7 0.2 0.7 1.3

9 3 1

a b c

a b c y x x

a b c

4. 2

100 10 40

400 20 160 0.4

25 5 10

a b c

a b c y x

a b c

5. 2

16 4 371

4 2 11 7 12

0 0 1

a b c

a b c y x x

a b c

6. 2

0 0 0

7 2 5

36 6 42

a b c

a b c y x x

a b c

7. 22( 4) 3y x

8a. 23 78 500d t t b. 500 km; she was 500 km from Mars’ atmosphere when she fired her rockets c. 5 km; 20 km; pulling away d. she crashed because the distance is 0 at 11.5

minutes and 14.5 minutes e. f. [0, 11.5] 9a. 20.4 36 1000y x x b. 680 accidents c. 70 year old driver is safer d. 45 yr old

Answer Key

e. [16, 85] because f(85) = 830 10a. 22.4 24 60w t t b. 60 liters c. 5 minutes d. 0; yes

e. f. water does not drain at a constant rate 11a. 20.01 37c r r b.112 cents/km c. 40 60r d. no, vertex is at (50, 12) so 12 cents is the minimum value of the function e. minimum = 50 kph and cost would be 12 cents/km 12a. 280 120 610y x x 12b. 530 m; 610 m 12c. at about -1.812 km (3.312 km would be extraneous based on location of cannon and target) 12d. no, max height of projectile is 655 m 13a. 500 – 2x; 300 – 2x; they are linear 13b. (500 2 )(300 2 )A x x ; quadratic 13c. A(5)=142,100 yd2; A(10)=134,400 yd2, A(15)=126,900 yd2 13d. about 34.169 yds

13e. 13f. (200 25 34) yds 54.226 yds

14a. 20.01 0.03 0.45p d d 14b. $3.85 14c. 25 inch 14d. $0.45; packaging? 14e. discriminant = -0.171; since it is negative there is no solution 14f. the slopes are not close to being equal, therefore a linear model is not a good choice 14g. vertex = (1.5, 0.4275)

Answer Key

15a.

15b. 20.00025 0.6 365y x x 15c. check the table in the calculator 15d. discriminant is negative, so there are no x-intercepts 15e. 9,006 meters 15f. 36.024 meters Section 4.6

1. 4 16i 2. 7 8i 3. 17 19i 4. 21 6i 5. 4 2i 6. 16 2 16 2

5 5 5

ii

7. 11 3 11 3

17 17 17

ii

8.

47 21

50 50i 9.

54 80

17 17i 10.

1 1

3 3i 11. 61 12.

39

3

13. 83

3 14. 1 15. 1 16. 0 17. 1 i 18. 2 25 0x 19. 2 6 17 0x x 20. real

21. imaginary 22. real 23. neither 24. True; the imaginary part would have to be 0i. 25. True; ( )ai bi a b i 26. True; 2 2 2 2 2( )( )a bi a bi a b i a b

27. True; 2 2 2 2; ( )a bi a b a bi a b and 2 2 2 2( )a b a b

28. Sum is ( ) ( ) ( ) ( )

Conjugate of sum is ( ) ( )

Sum of conjugates is ( ) ( )

( ) ( )

a bi c di a c b d i

a c b d i

a bi c di

a c b d i

The conjugate sum and the sum of the conjugates are equal. 29.

2

2

Product is ( )( )

( ) ( )

Conjugate of product is ( ) ( )

Product of conjugates is ( )( )

( ) ( )

a bi c di ac adi bci bdi

ac bd ad bc i

ac bd ad bc i

a bi c di

ac adi bci bdi ac bd ad bc i

The conjugate of the product is equal to the

product of the conjugates. 30. 0 0h ; which means it is not possible

Answer Key

Section 4.7

1. 3 7

2

ix

2. 1 or 6x 3.

2 17

2

ix

4.

5 65

10x

5. True

6. False; If d is a perfect square the solution will be rational. 7. False, 2x is already a square

8. 25c 9. 9

64c 10. Mountain View to Capital City is about 382.5 miles; Capital City to

Rapid City is about 221.5 miles Section 4.8 1. discriminant= 33; two real solutions 2. discriminant= -215;two complex solutions

3. 6 30 4. 1 19

2

i 5.

3 3 33

8

6.

2 17

2

i 7.

1 4 22

9

8.

2 34

2

9. 27 9 6 0x x 10. 28 3 11 0x x 11a. k < 0 or k > 1 11b. k = 0 or k = 1

11c. 0 < k< 1 12a. 1 1

3 3k 12b.

1 1or

3 3k 12c.

1 1or

3 3k k

13. discriminant = 2 24q p ; two real solutions 14. discriminant = 2 24p q ; two non-real

solutions 15a. 20.0001 55 150000P x x 15b. max at 275000; p(275000)=$82.50 15c. not possible to have 10 million dollar profit because when you solve the equation

20.0001 55 150000 10000000x x you get two non-real solutions. 16a. 15.22 sect 16b. 2.62 sect Section 4.9

1. 3 or 3x x 2. 5

63

x 3. 3 or 4x x 4. all real numbers 5. 8 6

5 5x

6. no solution 7. 3

105

x 8. 2 or 2x x 9. 1x 10. no solution

11. 2 < x < 8.0424 by solving the inequality

22

2

40(10 )( 2) 5 ft

2 2 3

5 100 251 12 0

8 2 3 2

xx x

x x

Answer Key

Section 9.1

1. (7,0) 2. (9, 3) 3. 1 1(2 , 2 )m mx x y y 4. 7 7 5 3 13 5

, ; , ; ,4 4 2 2 4 4

5. 3 9 3 1 3

, ; 1, ; ,2 4 2 2 4

6. 1 2 1 2 1 2 1 2 1 2 1 23 3 3 3, ; , ; ,

4 4 2 2 4 4

x x y y x x y y x x y y

7a.. distance between endpoint and trisection point is

2 2

2 1 2 1

2 2

2 1 2 1

3 3

1

3

x x y yd

x x y y

7b. 2nd trisection point is 1 2 1 22 2,

3 3

x x y y

8. 5 4

2, ; 3,3 3

9.4 2

, 2 ; , 13 3

10a. 15

3 55 10b.

2

3 3

1

m

m

10d. The graph approaches y = 3. 11a. y x

11b. 1y 11c. 10 5

( 4)3 2

y x 12. 4 or 8y 13. 11 or 13x 14. 4 609y

15. 17, 20 and 29 16. 2 triangles possible, vertices 2 3,2 17a. 50t 17b. 250 miles

17c. after 2 hours 14d. 50 miles per hour Parabolas - Sections 9.2 and 9.6 1. 2 16y x 2. 2 12x y 3. 2 16x y 4. 2 14( 0.5)x y 5. 2( 2) 8( 3)x y

6. 2( 2) 8( 4)y x 7. 2( 3) 4( 3)x y 8. 2( 2) 16( 1)y x 9. 2 4.5y x 10. (0,0); (0, 1); : 1V F d y 11. (0,0); (0.75,0); : 0.75V F d x 12. (2, 3); (2, 4); : 2V F d y 13. ( 5, 3); ( 5.5, 3); : 4.5V F d x 14. (0,2); ( 1,2); : 1V F d x 15. ( 3, 2); ( 3, 1); : 3V F d y

16. 2( 1) 4( 3)y x 17a. 2 49( 3) ( 4)

6x y 17b.

233,1

24

17c. 1

624

y 17d. 193

24

17e. 193

24 17f. They are the same 18. 5 feet 19. 22304 7238.23 ft 20. 4 2y x

21a. 2 640x y 21b. 8 feet 22a. 2x t 22b.see table below 22c. yes t -3 -2 -1 0 1 2 3 x 9 4 1 0 1 4 9 y -3 -2 -1 0 1 2 3

23a. 2 20.5( 1) 1 0.5 0.5y t t t 23b. see table below 23c. yes t -3 -2 -1 0 1 2 3 x -3 -2 -1 0 1 2 3 y 7 3.5 1 -0.5 -1 -0.5 1

Answer Key

Circles - Section 9.3 and 9.6 1. 2 2( 2) ( 2) 5x y 2. 2 2( 3) ( 1) 9x y 3. 2 2( 3) ( 1) 49x y

4. 2 2( 4) ( 5) 25x y 5a. 2

2 2 ( 1)4

y x 5b. 3

3 ( 5)4

y x

6a. ( 2, 1); 5C r 6b. int . 2 2 6; int . 1 21x y 6c. :[ 7,3]; :[ 4,6]D R

6d. not a function 7. 16 7

(0, 3) and ,5 5

8a. 2( ) (4 ) 16A x x x 8b. 2x

9. 10. 11. 12.

13a. length = 2x; width = 22 2 36y x 13b. 24 36A x x 13c. 72 units2

14a. slope = -2/3; equation of line: y = (3/2)x 14b. (6, 9) 14c. 2 2 117x y

15a. 5 169

12 12y x 15b.

212 169

5x

xm

x

15d. xm approaches a value of about 0.4; this is

almost equal to the slope 16. 2 2

2 41 1300

7 7 49x y

Ellipses - Section 9.4 and 9.6

1. 2.

3. 4.

5. 2 2

19 49

x y 6.

2 2

1169 31

x y 7.

2 2

136 24

x y 8.

2 2

1169 81

x y

9. 2 2

116 36

x y 10.

2 2 2 2

2 22 2

4 4 41 or 1

9 194 4

x y x y

h h h h

vertices: ( 9/2, 0); co-vertices: (0, 5/3);

foci: 629( ,0)6

vertices: ( 10,0)

co-vertices: (0, 2 2) ;

foci: ( 2,0)

vertices: (0, 5/2); co-vertices: ( 4/3, 0);

foci: 161(0, )6

vertices: ( 3, 0); co-vertices: (0, 1);

foci: ( 2 2,0)

Answer Key

#11 #12 #13 #14 standard equation 1

1625

22

yx

19

)4(

4

)3( 22

yx

125100

22

yx

1425

22

yx

x–radius 5 2 10 5 y–radius 4 3 5 2 focal radius

3 5 35 21

center (0, 0) (3, 4) (0, 0) (0, 0) vertices (5, 0), (–5, 0),

(0, 4), (0, –4) (5, 4), (1, 4), (3, 1), (3, 7)

(10, 0), (–10, 0), (0, 5), (0, –5)

(5, 0), (–5, 0), (0, 2), (0, –2)

foci (3, 0), (–3, 0) (3, 54 ) ( 35 , 0) ( 21 , 0) x–int. (5, 0), (–5, 0) none (10, 0) (–10, 0) (5, 0) (–5, 0) y–int. (0, 4), (0, –4) none (0, 5) (0, –5) (0, 2) (0, –2) #15 #16 #17 #18 standard equation 1

416

)3( 22

yx 1

9

)2(

16

)1( 22

yx 1

9

)2(

4

)5( 22

yx 1

4

)3(

36

)6( 22

yx

x–radius 4 4 2 6 y–radius 2 3 3 2 focal radius

32 7 5 24

center (–3, 0) (–1, 2) (–5, 2) (–6, –3) vertices (1, 0), (–7, 0),

(–3, 2), (–3, –2) (–5, 2), (3, 2), (–1, 5), (–1, –1)

(–3, 2), (–7, 2), (–5, 5), (–5, –1)

(0, –3), (–12, –3), (–6, –5), (–6, –1)

foci (–3 32 , 0) ( 71 , 2) 52,5 ( 246 , –3) x–int. (1, 0), (–7, 0)

0,

3

543

0,

3

5215

none

y–int (0,

4

7 )

4

1538,0

none (0, –3)

11. 12. 13.

Answer Key

14. 15. 16.

17. 18.

.

19. 19

)12(

5

)4( 22

yx

20. 11216

22

yx

21. 125

)7(

4

)5( 22

yx

22. 198

22

yx

23. 19

)2(

25

)1( 22

yx

24.

6

36

36

49

2

2

2

r

r

r

r

25a. (20 )A a a 25b. 2 2

1196 36

x y 25c. see table below 26. 32

a 7 8 9 10 11 12 13

A 285.88 301.59 311.02 314.16 311.02 301.59 285.88

25c. Because the maximum area occurs when a 10 and a b 20, b is also 10. So, the

equation becomes 2 2

2 21 100100 100

x yx y which is the equation of a circle.

Hyperbolas - Lesson 9.5 and 9.6

31. (0,0); . : ; ( 5,0); ( 34,0); . :

5

2. (0,0); . : ; (0, 4); (0, 2 5); . : 2

3. (0,0); . : ; (0, 3); (0, 10); . : 3

4. (0,0); . : ; ( 2,0); ( 6,0

C Tran axis x axis V F Asy y x

C Tran axis y axis V F Asy y x

C Tran axis y axis V F Asy y x

C Tran axis x axis V F

); . : 2Asy y x

Answer Key

1.

O

2.

O

3.

O

4.

O

2 2 2 2 2 2 2 2 2 2

2 2 22 2 2

2 2 2 2

( 4) ( 3)5. 1 6. 1 7. 1 8. 1 9. 1

16 20 4 5 36 9 9 16 4 12

( 4) ( 7) ( 4)10. ( 1) 1 11. ( 5) 1 12. ( 3) 1

8 3 8

( 1) ( 1) ( 1) 9( 1)13. 1 14. 1

4 9 4 16

15. ( 3,1); . : 1; ( 7,1),

y x x y y x x y y x

y y xx x y

x y y x

C Tran axis y V

22

5(1,1); ( 3 41,1); . : 1 ( 3)

49

16. ( 1, 2); . : 1; ( 1, 11), ( 1,7); ( 1, 2 106); . : 2 ( 1)5

( 2)17. ( 1) 1; ( 1, 2); . : 2; ( 2, 2), (0, 2); ( 1 3, 2);

2

(. : 2 2( 1) 18.

F Asy y x

C Tran axis x V F Asy y x

yx C Tran axis y V F

yAsy y x

2

21)( 2) 1; ( 2,1); . : 2;

4

( 2,3), ( 2, 1); ( 2,1 5); . : 1 2( 2)

19. ) ( 5,0), (5,0) ) 2 2 4 8, 8 5 8 13

x C Tran axis x

V F Asy y x

a Q R b PR PQ a then PR PQ

Answer Key

20 21. 22. 23.

. 24. 25. 26.

#20 #21 #22 #23 standard equation

2 2

125 16

x y

2 2

19 16

x y

2 2( 2) ( 3)1

36 25

x y

2 2( 3) ( 6)1

36 64

x y

x–radius 5 3 6 6 y–radius 4 4 5 8 focal radius 41 5 61 10

center (0, 0) (0, 0) (2, 3) (3, –6) vertices ( 5 , 0) 0, 4 (8, 3) and (–4, 3) (3, 2) and (3, –14)

foci ( 41 , 0) 0, 5 (2 61 , 0) (3, 4) and (3, –16)

transverse axis

horiz., length = 10

vert., length = 8

horiz., length = 12

vert., length = 16

conjugate axis

vert., length = 8

horiz., length = 6

vert. , length = 10 horiz. , length = 12

asymptotes 4

5y x 4

3y x 5

3 26

y x 46 3

3y x

x–intercepts

(5, 0), (–5, 0)

none 6 342 ,0

5

none

y–intercepts

none (0, 4), (0, –4) none 0, 6 3 10

Answer Key

#24 #25 #26 standard equation

2 2( 1) ( 4)1

16 1

x y

2 2( 3) ( 2)1

16 36

x y

2 21

144 25

x y

x–radius 4 4 12 y–radius 1 6 5 focal radius 17 2 13 13 center (1, 4) (3, –2) (0, 0) vertices (5, 4) and (–3, 4) (7, –2) and (–1, –2) (12, 0) and (–12, 0) foci ( 5 17 , 4) ( 3 2 13 , 4) (13, 0) and (–13, 0) transverse axis

horiz., length = 8 horiz., length = 8 horiz., length = 24

conjugate axis

vert. , length = 2 vert. , length = 122 vert., length = 10

asymptotes 16 1

4y x 3

2 32

y x 5

12y x

x–intercepts

(2, 0) and (0, 0) 4 103 ,0

3

(12, 0) and (–12, 0)

y–intercepts

none none none

27. 2 2

19 7

x y 28.

2 21

16 4

x y 29.

2 2( 2) ( 1)1

39 25

x y

30.

2 2( 3) ( 3)1

9 16

x y

31. 2 2( 2) ( 5)

136 64

x y

Conics Challenges and Extras 1. 2 4 ( )y h x h , where h is the x-coordinate of the vertex and the focal radius

2. 2 2( 6) ( 2)

19 7

x y 3. if 8, then the graph would be the point (1, – 2); if greater than 8,

there would be no graph since the equation would have no solution

4. 2 (3 3) 12x y 5. 25

0,3

6. length = 4p

Answer Key

7a. Endpoints of latera recta: 9 9 9 9

, 7 , , 7 ; , 7 ; , 74 4 4 4

7b. Endpoints of latera recta:

4 4 4 4, 5 , , 5 ; , 5 ; , 5

3 3 3 3

7c. Endpoints of latera recta:

3 5 3 5 3 5 3 52, , 2, ; 2, ; 2,

5 5 5 5

7d. First solve for y in the equation 2 2

2 21

x y

a b to obtain the positive solution

2

21

xy b

a .

This represents half the length of the latus rectum. Because the focus ( ,0)c and the latus rectum directly above the focus have the same x–coordinate, substitute c for x in the equation for y to get

2

21

cy b

a . Add the expressions underneath the radical to get

2 2

2

a cy b

a

. Then notice

that for an ellipse, a2 c2 b2. So, the equation for y simplifies to 2 2

2

b by b

a a . Therefore,

the length of the latus rectum is 22b

a 8. The eccentricity is

ce

a . Solve this equation for c

and then square each side to obtain 2 2 2e a c . You know that for an ellipse, 2 2 2c a b . Substitute e2a2 for c2 and solve for b2 to obtain 2 2 2(1 )b a e . Now substitute this expression for

b2 in the equation for an ellipse to obtain 2 2

2 2 21

(1 )

x y

a a e

. As e approaches 0 and a remains

fixed, the ellipse approaches the shape of a circle. 9a. apogee: about 405,508 km 9b. perigee: about 363,292 km 9c. The apogee A is A a c. The perigee P is P a c.

Substitute these values for A and P into ( ) 2

2

A P a c a c c ce

A P a c a c a a

Lesson 9.7

1. (5, 9), (3, 7) 2. (3, 1), (1, 3) 3. no points of intersection 4. ( 10,2), ( 10,2)

5. 9 4 6 9 4 6

, , ,5 5 5 5

6. (1.5, 1.5), ( 6, 69) 7. (), (), (), () 8. about 53.2 mi

9. yes; about 2.39 ft by 2.39 ft by 6.13 ft; or 4.35 ft by 4.35 ft by 1.85 ft

10. 4 5b