Foundations of Math 2 Final A. Which graph would best represent the graph of this parabola if it is translated 4 units down and 6 units left?

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1 Name: Date: 1. The graph of y = x 2 + is shown below. Which graph would best represent the graph of this parabola if it is translated units down and 6 units left? 2. The roots of a quadratic equation can be found using the graph below. What are the roots of this equation? page 1

2 3. If (3 + 2i) + (2 + bi) = 5 i, the value of b is A. 2 B. 2 C. 6 D. 6. The solution of the quadratic equation 2x 2 x 1 = 0 is A. 1 ± B. 1 ± 111 C. 1 ± 113 D. 1 ± Solve the following system for x and y. y = x x + 1 y x = 6. If x 3 is a factor of x 2 + x 12, then the other factor is A. x 3 B. 3x C. x D. x + 7. What is the vertex of the graph of the equation y = 3x 2 + 6x + 1? 8. What is the solution of the equation 2x 3 3 = 6? page 2

3 9. The solution of the quadratic equation x 2 + 3x 5 = 0 is 10. Solve the system: y = x 2 y = 2 x 11. The expression 3 6a 16 is equivalent to 12. If x is a real number, what is the solution set of the equation 1 2x = 2? 13. The expression (3x + )(2x 6) is equivalent to 1. The expression i 10 is equivalent to A. 1 B. i C. 1 D. i 15. If 2x = 5, then x is equal to page 3

4 16. The solution set of the equation x + 3 = 3 x is 17. The value of (5i 3 ) 3 is A. 15i B. 15i C. 125i D. 125i 18. The equation y = x 2 2x + 8 is graphed on the set of axes below. Based on this graph, what are the roots of the equation x 2 2x + 8 = 0? 19. In simplest form, 300 is equivalent to page

5 20. Which expression is equivalent to x 2 + 7x + 6? A. (x + 6) (x + 1) B. (x + 3) (x + 2) C. (x + 1) (x + 7) D. x (x + 7) 21. The sum of 3x 2 + x 7 and x can be expressed as A. x + x 3 B. 3x 2 + x + 3 C. 3x + x 3 D. x 2 + x The point (3, 2) is rotated 90 about the origin and then dilated by a scale factor of. What are the coordinates of the resulting image? 23. Which expression is a solution for the equation 2x 2 x = 7? A. 1 ± 57 2 B. 1 ± 57 2 C. 1 ± 57 D. 1 ± A ball is thrown straight up at an initial velocity of 5 feet per second. The height of the ball t seconds after it is thrown is given by the formula h(t) = 5t 12t 2. How many seconds after the ball is thrown will it return to the ground? page 5

6 25. The solution to the quadratic equation 2x 2 + 5x 1 = 0 is A. 5 ± 17 B. 5 ± 17 C. 5 ± 33 D. 5 ± Noj is 5 years older than Jacob. The product of their ages is 8. How old is Noj? 27. The solution set of the equation x + 6 = x is 28. As shown on the graph below, R S T is the image of RST under a single transformation. Which transformation does this graph represent? page 6

7 29. What are the vertex and axis of symmetry of the parabola y = x 2 16x + 63? 30. Given point A( 2, 3). State the coordinates of the image of A under the composition T 3, r x axis. a. (-5, 1) b. (-5, -7) c. (5, 7) d. (5, -1) 31. Written in factored form, the trinomial 3x 2 + 5x 2 is equivalent to A. (3x + 1)(x 2) B. (3x 1)(x + 2) C. (3x + 2)(x 1) D. (3x 2)(x + 1) 32. Triangle ABC is drawn in Quadrant III. If ABC is reflected in the y-axis, its image will lie in Quadrant 33. The product of (3 2i) and (7 + 6i) is A i B i C. 9 + i D i page 7

8 3. In the accompanying diagram, A B C is the image of ABC. Which type of transformation is shown? 35. What is expressed in simplest radical form? 36. What is the y-intercept of the parabola whose equation is y = x 2 + 5x 6? 37. What is the solution set of the equation x + 1 = x 1? 38. A cliff diver on a Caribbean island jumps from a height of 105 feet, with an initial upward velocity of 5 feet per second. An equation that models the height, h(t), above the water, in feet, of the diver in time elapsed, t, in seconds, is h(t) = 16t 2 + 5t How many seconds, to the nearest hundredth, does it take the diver to fall 5 feet below his starting point? page 8

9 39. Consider the graph of the equation y = ax 2 + bx + c, when a 0. If a is multiplied by 3, what is true of the graph of the resulting parabola? 0. Which is an equation of the axis of symmetry of the parabola whose equation is y = 2x 2 3x +? A. x = 3 B. x = 3 C. y = 3 D. y = 3 1. Which graph could be used to find the solution of the system of equations y = 2x + 6 and y = x 2 + x + 3? 2. The best description of a dilation of a figure is A. an enlargement or a reduction of the figure B. a slide of the figure C. a turning of the figure about some fixed point D. a mirror image of the figure 3. Which is an equation of the axis of symmetry of the graph of the equation y = 2x 2 5x + 3? A. x = 5 2 B. x = 5 2 C. x = 5 D. x = 5. The expression written in simplest radical form is page 9

10 5. If the coordinates of point A are ( 2, 3), what is the image of A under r y axis D 3? 6. Expressed in factored form, the binomial 2x 2 y xy 3 is equivalent to 7. Which transformation is not always an isometry? 8. Which shape does not have rotational symmetry? 9. In the accompanying diagram, which point may be the image of point A after a line reflection in the x-axis? y B A E x C D 50. The height of a swimmer s dive off a 10-foot platform into a diving pool is modeled by the equation y = 2x 2 12x + 10, where x represents the number of seconds since the swimmer left the diving board and y represents the number of feet above or below the water s surface. What is the farthest depth below the water s surface that the swimmer will reach? page 10

11 51. If x = 7, what is the value of x? 52. The greatest common monomial factor of 12x 2 and 8x 3 is 53. An archer shoots an arrow into the air such that its height at any time, t, is given by the function h(t) = 16t 2 + kt + 3. If the maximum height of the arrow occurs at time t =, what is the value of k? 5. Two equations were graphed on the set of axes below. Which point is a solution of the system of equations shown on the graph? page 11

12 55. The roots of the equation 2x 2 + 7x 3 = 0 are 56. What is the value of x in the equation 3 + x 5 = 2? 57. The solution set of the equation x = 0 is A. Ø B. {2} C. { 26} D. {0} 58. The expression 3i(2i 2 5i) is equivalent to 59. Which expression is equal to (x + 3) 2? A. x B. x C. x 2 + 6x + 9 D. x 2 + 3x The sum of 18 and 72 is A. 6i B. 36i C D. 9i 2 page 12

13 Problem-Attic format version..279 c EducAide Software Licensed for use by kellyc.taylor@cms.k12.nc.us Terms of Use at 01/10/ Objective: A.07C 2. 1 and 3.. C C 5. ( 9, 13), ( 2, 6) Objective: L.03C 6. D 7. ( 1, 2) ± ( 2, ), (1, 1) Objective: L.03C a 5 3 a { 3 2 } 13. 6x 2 10x 2 1. C {1} C 2 and i A D 22. (8, 12) 23. D D {3} 28. rotation 29. vertex: (8, 1); axis of symmetry: x = ( 5, 7) B IV B reflection

14 Teacher s Key Page {3} The new parabola is narrower than the original parabola. B 52. x (8, 9) ± 73 A 15 6i C D A D (6, 9) 6. 2xy(x 2y 2 ) dilation trapezoid D 8 feet