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