Algebra II B Quiz Make-up

Transcription

1 Class: Date: Algebra II B Quiz Make-up Graph each function. How is each graph a translation of f(x) = x 2? 1. y = x 2 4 a. c. b. f(x) translated down 4 unit(s) d. f(x) translated up 4 unit(s) f(x) translated to the left 4 unit(s) f(x) translated to the right 4 unit(s) 1

2 2. y = (x + 2) 2 a. c. b. f(x) translated to the right 2 unit(s) d. f(x) translated down 2 unit(s) f(x) translated to the left 2 unit(s) f(x) translated up 2 unit(s) 2

3 3. y = (x + 3) a. c. b. f(x) translated up 3 unit(s) and translated to the left 3 unit(s). d. f(x) translated down 3 unit(s) and translated to the left 3 unit(s) f(x) translated up 3 unit(s) and translated to the right 3 unit(s) f(x) translated down 3 unit(s) and translated to the right 3 unit(s) 3

4 4. Identify the vertex and the axis of symmetry of the graph of the function y = 3(x + 2) 2 3. a. vertex: (2, 3); axis of symmetry: x = 2 b. vertex: ( 2, 3); axis of symmetry: x = 2 c. vertex: ( 2, 3); axis of symmetry: x = 2 d. vertex: (2, 3); axis of symmetry: x = 2 5. Identify the maximum or minimum value of the graph of the function y = 2(x 3) 2 2. a. maximum value: 2 domain: all real numbers 2 range: all real numbers b. maximum value: 2 domain: all real numbers range: all real numbers 2 c. minimum value: 2 domain: all real numbers 2 range: all real numbers d. minimum value: 2 domain: all real numbers range: all real numbers 2 4

5 6. Which is the graph of y = 2(x 3) 2 5? a. c. b. d. 7. What steps transform the graph of y = x 2 to y = 2(x + 2) 2 5? a. translate 2 units to the right, translate up 5 units, stretch by the factor 2 b. reflect across the x-axis, translate 2 units to the right, translate up 5 units, stretch by the factor 2 c. reflect across the x-axis, translate 2 units to the left, translate down 5 units, stretch by the factor 2 d. translate 2 units to the left, translate down 5 units, stretch by the factor 2 5

6 8. Use the vertex form to write the equation of the parabola. a. y = (x + 3) 2 2 c. y = 3(x + 3) 2 2 b. y = 3(x 3) 2 2 d. y = 3(x 3) Suppose a parabola has vertex ( 1, 7) and also passes through the point (0, 5). Write the equation of the parabola in vertex form. a. y = 2(x 1) 2 7 c. y = 2(x + 1) 2 7 b. y = (x + 1) 2 7 d. y = 2(x + 1) Suppose a parabola has an axis of symmetry at x = 4, a maximum height of 3 and also passes through the point ( 3, 1). Write the equation of the parabola in vertex form. a. y = (x + 4) c. y = 4(x 4) b. y = 4(x + 4) d. y = 4(x + 4) 2 3 What are the vertex and the axis of symmetry of the equation? 11. y = 2x x 14 a. vertex: ( 8, 142) axis of symmetry: x = 142 b. vertex: ( 8, 142) axis of symmetry: x = 8 c. vertex: ( 8, 142) axis of symmetry: x = 142 d. vertex: ( 8, 142) axis of symmetry: y = 8 6

7 12. y = 2x x 14 a. vertex: ( 5, 36) axis of symmetry: y = 5 b. vertex: ( 5, 36) axis of symmetry: x = 5 c. vertex: ( 5, 36) axis of symmetry: x = 5 d. vertex: ( 5, 36) axis of symmetry: x = 36 What is the maximum or minimum value of the function? 13. y = 2x x y = 2x x 2 7

8 What is the graph of the equation? 15. y = x 2 4x + 5 a. c. b. d. 8

9 16. y = x 2 + 2x + 3 a. c. b. d. 9

10 17. y = 2x 2 2x 1 a. c. b. d. 10

11 18. You live near a bridge that goes over a river. The underneath side of the bridge is an arch that can be modeled with the function y = x x where x and y are in feet. How high above the river is the bridge (the top of the arch)? How long is the section of bridge above the arch? a. The bridge is about ft above the river and the length of the bridge above the arch is about ft b. The bridge is about ft above the river and the length of the bridge above the arch is about ft c. The bridge is about ft above the river and the length of the bridge above the arch is about ft d. The bridge is about ft above the river and the length of the bridge above the arch is about ft What is the expression in factored form? 19. x x + 42 a. (x 7)(x 6) c. (x + 6)(x 7) b. (x + 7)(x 6) d. (x + 6)(x + 7) 20. x 2 10x + 21 a. (x 3)(x 7) c. (x + 7)(x + 3) b. (x 7)(x + 3) d. (x 3)(x + 7) 21. x 2 + 5x + 14 a. (x + 2)(x + 7) c. (x 7)(x 2) b. (x 7)(x + 2) d. (x 2)(x + 7) What is the expression in factored form? 22. 8x 2 + 4x a. 2x(4x + 2) c. 2x(4x 2) b. 2(4x + 2) d. 2x(4x + 2) 11

12 23. 5x x + 60 a. 5(x 4)(x + 3) c. 5(x 4)(x 3) b. 5(x + 4)(x 3) d. 5(x + 4)(x + 3) 24. 4x x + 40 a. 4(x + 5)(x + 2) c. 4(x 5)(x + 2) b. 4(x + 5)(x 2) d. 4(x 5)(x 2) 25. 5x x + 28 a. (5x + 7)(x + 4) c. (x + 7)(5x + 4) b. (5x + 7)(x 4) d. (5x + 4)(x 7) 26. 5x 2 38x 63 a. (x + 7)(5x 9) c. (5x 9)(x 7) b. (5x + 7)(x 9) d. (5x + 7)(x + 9) 27. 4x 2 16x + 16 a. (2x 4)( 2x + 4) c. (2x 4) 2 b. ( 2x 4) 2 d. (2x + 4) x 2 8x + 4 a. (2x 2) 2 c. (2x + 2) 2 b. ( 2x 2) 2 d. ( 2x + 2)(2x 2) 12

13 29. x 2 16 a. (x + 4)( x 4) c. (x + 4)(x 4) b. ( x + 4)(x 4) d. (x 4) x 2 16 a. (3x 4) 2 c. (3x + 4)(3x 4) b. (3x + 4)( 3x 4) d. ( 3x + 4)(3x 4) What are the solutions of the quadratic equation? 31. x x = 48 a. 6, 8 c. 6, 8 b. 6, 8 d. 6, x 2 11x + 24 = 0 a. 8, 3 c. 8, 3 b. 8, 3 d. 8, x x + 15 = 0 a. 3, 5 2 c. 5 2, 2 3 b. 3, 2 d. 3, x 2 18x + 9 = 0 3 a. 5, 5 3 b. 3, 3 5 c. 3, 5 d. 3,

14 35. How would you translate the graph of y = x 2 to produce the graph of y = x ? 14

15 36. Graph the quadratic function. Label the vertex and axis of symmetry. y = x 2 2x 4 15

16 37. Find the vertex and the axis of symmetry of the parabola. y = 3x x Find the vertex of the parabola and determine if it opens up or down. y = 7 8x 2x Find the vertex and the axis of symmetry of the parabola. y = 3x x

17 40. Graph the function. Label the vertex, axis of symmetry, and x-intercepts. y = x 2 4x + 2 Find the maximum value or minimum value for the function. 41. f( x) = x 2 + 6x

18 42. f( x) = 4x 2 + 6x f( x) = x 2 + 7x f( x) = 2x 2 + 5x How would you translate the graph of y = x 2 to produce the graph of y = ( x 7) 2? 46. How would you translate the graph of y = x 2 to produce the graph of y = ( x 6) 2? a. translate the graph of y = x 2 left 6 units b. translate the graph of y = x 2 right 6 units c. translate the graph of y = x 2 down 6 units d. translate the graph of y = x 2 up 6 units 47. How would you translate the graph of y = x 2 to produce the graph of y = x 2 + 1? 18

19 48. Graph the function. Label the vertex, axis of symmetry, and x-intercepts. y = 2( x + 2) ( x + 4) a. c. b. vertex: ( 3, 2) axis of symm: x = 3 x-intercepts: 4, 2 d. vertex: (3, 2) axis of symm: x = 3 x-intercepts: 2, 4 vertex: ( 3, 2) axis of symm: x = 3 x-intercepts: 4, 2 vertex: (3, 2) axis of symm: x = 3 x-intercepts: 2, 4 19

20 Write in standard form and graph. 49. y = ( x 2) 2 3 a. y = x 2 4x + 7 c. y = x 2 4x 7 b. y = x 2 + 4x 7 d. y = x 2 + 4x

21 50. y = ( x 1) a. y = x 2 2x+ 1 c. y = x 2 + 2x+ 3 b. y = x 2 2x+ 3 d. y = x 2 + 2x Write as the product of two factors: x 2 + 3x 40 a. ( x 5) ( x + 8) c. ( x + 5) ( x 8) b. ( x 5) ( x 8) d. ( x + 5) ( x + 8) 52. What are the solutions of the equation? x 2 10x + 24 = 0 a. x = 1 or x = 24 c. x = 1 or x = 24 b. x = 4 or x = 6 d. x = 4 or x = Solve using factoring: x 2 2x 8 = 0 a. 2, 4 b. 2, 4 c. 2, 4 d. 4, 2 21

22 Find the zeros of the function. 54. y = x 2 11x A restaurant has a patio that is 8 feet wide and 12 feet long. The restaurant owners want to double the area of the patio by increasing the width and the length by the same distance x. Write an equation that x must satisfy. Can your equation be solved by factoring? Is there a single solution or more than one solution? Explain. 56. Write as the product of two factors: 12h 2 31h Write as a product of factors. 12x x

23 Factor the expression x 2 42x + 16 Solve. 59. x 2 6x = 0 a. 0, 6 c. 6, 6 b. 0, 6 d. 1, x 2 12x 16 = 0 23

24 Algebra II B Quiz Make-up Answer Section 1. A 2. B 3. A 4. B 5. D 6. D 7. D 8. C 9. C 10. B 11. B 12. B 13. minimum value: 52 range: y maximum: 96 range: y A 16. A 17. A 18. A 19. D 20. A 21. B 22. D 23. D 24. C 25. A 26. B 27. C 28. A 29. C 30. C 31. B 32. B 33. A 34. B 35. Move the graph of y = x 2 up 10 units to get the graph of y = x

25 36. axis of symmetry: x = 1 vertex: (1, 5) 37. Vertex: (2, 4); Axis: x = Vertex: (-2, 15); Opens down 39. Vertex: (-2, -3); Axis: x = vertex: Ê Ë Á 2, 6ˆ ; axis of symmetry: x = 2;x-intercepts at 4.4, maximum: minimum: minimum: maximum: translate the graph of y = x 2 right 7 units 46. B 47. translate the graph of y = x 2 up 1 unit 48. A 49. B 50. B 51. A 52. D 53. C 2

26 54. 9, ( x + 8) ( x + 12) = 192 Yes. The equation to be solved is x x 96 = 0. Because x x 96 = ( x 4) ( x + 24) the solutions to the equation are x = 4 or x = 24. Since the answer cannot be negative, there is only one solution: the patio should be increased by 4 feet in each direction. 56. ( 4h 5) ( 3h 4) 57. y = ( 3x + 4) ( 4x + 3) 58. (x 8)(5x 2) 59. A 60. 1, 4 3