Chapter 5 solutions Section 5.1 Answers 1 v(-6, 0), Domain: ARN , Range: y>0

2 v(4, 0), Domain: ARN , Range: y>0

3. v(0, 3), Domain: ARN , Range: y<3

4. v(0, -2), Domain: ARN , Range: y>-2

5. v(-3, 7), Domain: ARN , Range: y<7

6. v(1, -6), Domain: ARN , Range: y>-6

7. v(0, 0), Domain: ARN , Range: y>0

8. v(0, 0), Domain: ARN , Range: y>0

9. v(0, 0), Domain: ARN , Range: y>0

10. upside down 11. (h, k) 12. all real numbers 13. narrower 14. wider 15. (9, 7) Graphing Calculator section 16. v(-!

!, 0), Domain: ARN , Range: y<0

17. v(4, !!), Domain: ARN , Range: y>!

!

18. v(!!, !!!

), Domain: ARN , Range: y>!!!

19.

20.

21. the graph in question 20 has the points with negative y values reflected over the x-axis

Section 5.2 Answers

5. v(2, 5), Domain: ARN , Range: y>5

6. v(-3, 0), Domain: ARN , Range: y<0

7. v(0, 4), Domain: ARN , Range: y>4

8. v(-1, -2), Domain: ARN , Range: y>-2

9. v(7, 0), Domain: ARN , Range: y<0

10. v(8, 6), Domain: ARN , Range: y<6

Section 5.3 solutions

1. v(-2, -4), roots (-4,0) and (0,0) Domain ARN range y>-4

2. v(0,9), roots (-3,0) and (3,0) Domain: ARN , Range: y<9

3. v(-1, 0), roots (-1,0) Domain: ARN , Range: y>0

4. v(3,4), roots (1,0) and (5,0) Domain: ARN , Range: y<4

5. v(-3, -4), roots (--2.27,0) and (-5.73,0) Domain: ARN , Range: y>-3

6. v(0.65, -7.23), roots (-0.2,0) and (1.5,0) Domain: ARN , Range: y>-7.23

7. v(1.5, 6), roots (0.28,0) and (2.72,0)Domain: ARN , Range: y<6

8. v(4,12), no roots Domain: ARN , Range: y>12

11. a changes the width (or breadth) of the parabola. If |a| > 1, then the parabola is wider than y=x2 . If 0 < |a| < 1, then the parabola will be narrower. 12. If a is negative, then if flips the parabola upside-down. 13. h shifts the parabola to the right or left. If h is negative in the equation, it will shift the parabola to the right. If it is positive, it will shift the parabola to the left. 14. k shifts the parabola up and down. If k is negative in the equation, it will shift the parabola down. If it is positive, it will shift the parabola up. 15. The maximum height is the y-coordinate of the vertex or 144.8 feet. The ball travelled a total distance of 436.6 feet. Section 5.4 solutions

1.v(3,0), roots (3,0) double root Domain: ARN , Range: y>0

2.v(0,1), roots = no roots Domain: ARN , Range: y>1

3.v(-1, -4), roots (1,0) and (-3,0) Domain: ARN , Range: y>-4

4. v(0,3), roots (1,0) and (-1,0) Domain: ARN , Range: y<3

5. v(-4,-8), roots (-8,0) and (0,0) Domain: ARN , Range: y>-8

6. v(3, 9), roots (0,0) and (6,0) Domain: ARN , Range: y<9

Section 5.5 solutions 2.y=a(x–h)2+k3.y=!

!(x–1)2+1

4.y=-2(x+5)25.y=!

!(x-1)2-2

7.y=(x+8)2–548.y=-(x-4)2+19.y=(x+!

!)2+!

!

10.y=3(x+2)2–611.y=-5(x+1)2–712.y=2(x+!

!)2+!"

!

13..y=(x-1)2–4Roots(-1,0)and(3,0)y-intercept(0,-3)

14..y=-(x-2)2+1Roots(1,0)and(3,0)y-intercept(0,-3)

15..y=(x+!

!)2–!"

!Roots(!± !"

!,0)y-intercept(0,5)

16..y=-2(x-3)2+8Roots(1,0)and(5,0)y-intercept(0,-10)

17..y=4(x-5)2–4Roots(-6,0)and(-4,0)y-intercept(0,96)

18..y=3(x+!

!)2–!"

!Roots(-4,0)and(-1,0)y-intercept(0,12)

Section 5.6 solutions 1.(2,0)doubleroot 2.(-3,0)(-5,0) 3.(2,0)(-2,0) 4.(1,0)(5,0) 5.noroots 6.(-1.93,0)(2.59,0) 7.(-1.79,0)(4.46,0) 8.(-3.17,0)(33.17,0) 9.noroots 10.(-11.17,0)(-2.83,0) 11.Graph𝑦=3𝑥2−10𝑥 and𝑦=8 andlookforthepointsofintersection.Or,graph𝑦=3𝑥2−10𝑥−8 and𝑦=0 andlookforthepointsofintersection.12.Aquadraticequationhasonlyonevariable,whileaquadraticfunctionhas2variables.13.No,aquadraticequationcouldhave1solutionifthereisonly1x-interceptornosolutionsiftherearenox-intercepts.14.Thegraphof𝑦=𝑥2+4 showsnox-intercepts.15.Answersvary.Possibleanswer:Thegraphingmethodisaquickwaytosolvequadraticequations

5.7 Deriving and Using the Quadratic Formula Answers 1. x = −4 ± √7 2. x = 4 or x = !!

!

3. x =1 ±√41 4 4. x=!

! double root

5. x = -5 ± √13 2 6. x = 7; double root 7. x = 10 or x = -15 8. x = !

! or x = !!

!

9. x =!!!

0r x = -2 10. x = !!

! or x = !

!

11. x = 8±2 √15 12. x =± !"

!

13. 1 real solution 14. 2 real solutions

15. 2 imaginary solutions 16. 2 real solutions 17. 2 real solutions 18. 2 imaginary solutions 7. x = 20 or x =-3 19. c< 1, c = 1, c > 1 20. c< 9, c = 9, c > 9 21. c< 36, c = 36, c > 36 22. 4k2 −16 23. k> 2 and k < -2 24. k = 2 and -2, 25. -2 < k < 2 5.8 Solving Quadratics by Factoring Answers 1.x = -9 or x = 1 2. x = 0 or x = -6 3. x = !!

!, or x = 4

4. x =!! or x = !!

!

5. x = 3, -3 6. x = !!

! double root

7. not factorable 8. x = 0 or x =!

!

9. x = !!!

or x =-8 10. x = ± !

!

11. not factorable 12. x = -2, or x =!!

!

13. x = !!

! or x =!

!

14. x = !!!

or x = !!!

15. x = !

! or x = !

!

16. The length is 64 feet, the width is 39 feet. Section 5.9 Solutions 1. 3i 2. 11i 2 3. 18i 5 4. -84i 2 5. -12 6

6. -21 14 7. 1 8. -16 9. -9i 10. i 11. -2i

12. i !!

13. 17 – 12i 14. -6 – 7i 15. 5 + 10i 16. -1 – 6i 17. 0.8 + 0.5i 18. 22 – 13i 19. 11 + 35i 20. (7± 3𝑖, 0) 21.(!±!!

!, 0)

22. (-1, 0) (!

!, 0)

23. (2±5𝑖, 0) 24. (4±4 2, 0)

Section 5.10 solutions 1.m=252.m=1213.m= !

!"

4.m=!"

!

5.m=!

!

6.x=−9± 166

7.x=!± !"!

8.x=!± !"!

9..x=!± !"#!"

10.x=!± !"!

11.x=-2orx=4

12.x=-2± !!

13.x=1± !!

14.x=-1orx=!

!

15.x=!!± !"!

Section 5.11 solutions 1. a. 91 b. (3.5, -4) and (-1, -4) c. (3.91, 0) and (-1.41,0) 2. a. -33 b. imaginary solution c. (-1.5, 0) (2.5,0) 3. a. (-3, 0) and (-5, 0) b. (-4 ±√3, 2) c. (-4, -1) d. (0, 15) and (-8, 15) 4. a. yes b. no 5. a. yes b. yes 6. a. no b. yes 7. a. no b. no

Section 5.12 Solutions 1. y = 2(x -+ 4)2 + 3 2. y = !

!(x + 2)2 + 3

3. y = 3x2 – 2x + 5 4. y = !!

!x2 – 2x + 15

5. y = 0.2x2 + 0.7x + 1.3

6. y = 2x2 - 5 7. These points can not form a function because there are 2 values for y when x = 5 8.These point form a linear function

Section 5.13 Solutions 1 a. y = 0.4x2 - 36x + 1000 b.680 accidents /100 million km c. 70 year old drivers appear to be safer d. 45 year old drivers appear to be the safest e. 16 < y < 85 2a. d = -16t2 + 40t + 4 b. (1.25, 29) after 1.25 seconds the ball reaches a maximum height of 29 feet. c. It will hit the ground after 2.6 seconds d Domain 0 < t < 2.6 range 0 < h < 29 3a. h = -4.5t2 + 20t + 1.5 b. 2.22 s c. 23.72 m d. 1.5 m e. 4.52 s 4b. width = 30 – 2x length = 50 – 2x c. A = (30 – 2x)(50 – 2x) = 4x2 - 160x + 1500 d. (1, 1344) (2, 1196) (4, 924) e. 3.4 ft f. 5.42 ft 5a. V = 2.4t2 – 24t + 60 b. 60 L c. 5 minutes d. 0 L, it is reasonable f. When the water is deeper, the pressure is higher so the water drains faster. 6a. C = 0.01s2 -1s + 37 b. $1.12 per km c. between 40 and 60 km/h d. it is not possible (this value is below the vertex of the model) e. 50 km/h 7a. L(t) = 20 – 2t W(t) = 15 + 3t b. A(t) = -6t2 + 30t + 300 c. t = 2.5 min

d. t = 10 min. 8a. y = 900 – 2x linear function b. A(x) = -2x2 + 900x quadratic function c. A(100) = 70,000 ft2 A(300) = 90,000 ft2 d. 225 ft, A(225) = 101,250 ft2 e. x = 0 or x = 450 9. y = −0.07x2

+1.25x 10. y = −0.01x2

+ 0.98x +5.25 11. y = -0.18x2 + 8.52x – 3.95