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3/18/13 POW #16 - 2013 Teacher: Ms. Williams Name: ____________________________________ 1. 4. Factor: x 2 − x − 6 Factor: x 2 + 5x 1. 2. 3. 4. (x (x (x (x − 3) (x + 3) (x − 1) (x − 6) (x + 2) − 2) − 6) − 1) 1. 2. 3. 4. x(x + 5) 5(x + 1) x x+5 -------------- -------------- 2. 5. Factor: y2 - 100 Factor: x 2 + 6x + 8 1. 2. 3. 4. ( y - 10)2 ( y - 10)( y - 10) ( y + 10)( y + 10) ( y + 10)( y - 10) 1. 2. 3. 4. (x (x (x (x + 2)(x + 4) - 2)(x - 4) - 2)(x + 4) + 2)(x - 4) -------------- -------------- 3. 6. Express x 2 - 5x - 24 as the product of two binomials. Express 9 - y2 as the product of two binomial factors. 1. 2. 3. 4. (x (x (x (x - 8)(x + 3) + 8)(x - 3) + 6)(x + 4) - 6)(x - 4) -------------- www.castlelearning.com/review/teacher/AssignmentPrinting.aspx 1. 2. 3. 4. (3 + y)(3 - y) ( y + 3)(y - 3) (3 - y)(3 - y) ( y + 3)( y + 3) -------------- 1/10 3/18/13 POW #16 - 2013 7. 10. Factor: x 2 - 4x - 5 How many solutions are there to the following system of equations: 1. 2. 3. 4. (x (x (x (x + 5)(x + 1) + 5)(x - 1) - 5)(x + 1) - 5)(x - 1) -------------- 8. Which is a factor of x 2 + 5x - 24? 1. (x + 4) 2. (x - 4) 3. (x + 3) 4. (x - 3) -------------- 9. Factor completely: 2a2 + 2a - 84 1. 2. 3. 4. (2a - 7)(a + 6) 2(a - 7)(a - 6) 2(a - 7)(a + 6) 2(a + 7)(a - 6) -------------- y=6-x y = x 2 - 6x + 6 1. 2. 3. 4. 5. 1 2 3 4 0 -------------- 11. Factor completely: 2x 2 - 50 1. 2. 3. 4. (x + 5)(2x - 5) (2x + 5)(x - 5) 2(x - 5)2 2(x + 5)(x - 5) -------------- 12. Factor completely: 2x 2 - 18 1. 2. 3. 4. 2(x 2(x 2(x 2(x - 3)2 + 3)2 + 3)(x - 3) + 9)(x - 9) -------------- www.castlelearning.com/review/teacher/AssignmentPrinting.aspx 2/10 3/18/13 POW #16 - 2013 13. 16. Solve the following system of equations algebraically and check: Factor completely: 3x 2 + 15x - 42 y = x 2 + 2x - 4 y - 5 = 2x The solution with a positive value for y is ( , 1. 2. 3. 4. 3(x 2 + 5x - 14) 3(x - 7)(x + 2) 3(x + 7)(x - 2) 3(x + 14)(x - 1) -------------- ). 17. The solution with a negative value for y is ( , Solve the following system of equations: ). y = x 2 + 4x + 1 y = 5x + 3 -------------- 14. What are the factors of y3 - 4y? 1. (1,2) and (2,13) 3. (-1,-2) and (2,13) 2. (-1,-2) and (-2,13) 4. (-1,-2) and (-2,-13) -------------- 1. 2. 3. 4. y(y - 2)(y - 2) y(y + 4)(y - 4) (y2 + 1)(y - 4) y(y + 2)(y - 2) -------------- 18. Which is an equation of the line of symmetry for the parabola in the accompanying diagram? 15. What are the factors of x 2 - 10x - 24? 1. 2. 3. 4. (x (x (x (x - 4)(x + 6) - 4)(x - 6) - 12)(x + 2) + 12)(x - 2) -------------- 1. x = 2 2. x = 4 3. x = 3 4. y = 3 -------------- www.castlelearning.com/review/teacher/AssignmentPrinting.aspx 3/10 3/18/13 POW #16 - 2013 19. 23. Find the axis of symmetry for the quadratic equation y = Find the vertex for the quadratic equation and tell if the vertex is a maximum or a minimum: y = -(x + 2)2 - 4. −x 2 − 8x + 10. 1. (1, -4), maximum 3. (2, -4), minimum 2. (-2, -4), maximum Answer: x = 4. (-1, 2), minimum -------------- -------------- 24. 20. Find the turning point and the axis of symmetry for the quadratic equation y = x 2 − 4x + 8. 1. (2, 4) and y = 2 2. (2, 4) and x = 2 3. (4, 8) and x = 4 4. (−2, 20) and x = −2 -------------- 21. Find the turning point for the quadratic equation, y = 3x 2 + 6x - 2, and tell whether the point is a maximum or a minimum point. 1. (1, 5) and a minimum 3. (-1, -5) and a minimum 2. (-1, -5) and a 4. (-1, 5) and a maximum maximum -------------- 22. Find the vertex for the quadratic equation, y = -4x 2 4x + 1, and tell whether the point is a maximum or a minimum point. 1. (0.5, -4) and a 3. (0.5, 4) and a minimum minimum 2. (-0.5, -1) and a 4. (-0.5, 2) and a maximum maximum Solve the following system of equations algebraically. y = x 2 − 4x − 1 y=x−7 1. 2. 3. 4. (2, −5), only (2, −5) and (3, −4) (3, −4), only (−2, −9) and (3, −4) -------------- 25. Solve the following system of equations algebraically. y = x2 + x − 2 y = 1 + 3x 1. 2. 3. 4. (−1, −2), only (2, 7) and (−3, 4) (−3, −8) (3, 10) and (−1, −2) -------------- -------------- www.castlelearning.com/review/teacher/AssignmentPrinting.aspx 4/10 3/18/13 POW #16 - 2013 26. 29. Solve the following system of equations algebraically. What are the vertex and the axis of symmetry of the parabola shown in the diagram below? y = x 2 + 2x y = 2x + 4 1. 2. 3. 4. (−2, 8), only (−2, 0) and (2, 8) (2, 8), only (2, −8) and (−2, 8) -------------- 27. Graphically find the roots of the equation y = x 2 + 4x − 32. 1. 2. 3. 4. x x x x = −8, only = 8 and −4 = −8 and 4 = −8 and −4 -------------- 28. 1. The vertex is (-2,-3), and the axis of symmetry is x = -2. 2. The vertex is (-2,-3), and the axis of symmetry is y = -2. 3. The vertex is (-3,-2), and the axis of symmetry is y = -2. 4. The vertex is (-3,-2), and the axis of symmetry is x = -2. -------------- The expression x 2 − 1. 2. 3. 4. (x (x (x (x + 2)(x − 2)(x + 4)(x + 8)(x 16 is equivalent to − 8) + 8) − 4) − 8) -------------- www.castlelearning.com/review/teacher/AssignmentPrinting.aspx 5/10 3/18/13 POW #16 - 2013 30. 32. 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? 1. The vertex is 3 units above the vertex of the original parabola. 2. The new parabola is 3 units to the right of the original parabola. 3. The new parabola is wider than the original parabola. 4. The new parabola is narrower than the original parabola. The expression 9x 2 – 100 is equivalent to 1. (9x – 10)(x + 10) 2. (3x – 10)(3x + 10) 3. (3x – 100)(3x – 1) 4. (9x – 100)(x + 1) -------------- 31. A swim team member performs a dive from a 14-foothigh springboard. The parabola below shows the path of her dive. -------------- 33. What are the vertex and axis of symmetry of the parabola y = x 2 − 16x + 63? 1. 2. 3. 4. vertex: (8,−1); axis of symmetry: x = 8 vertex: (8,1); axis of symmetry: x = 8 vertex: (−8,−1); axis of symmetry: x = −8 vertex: (−8,1); axis of symmetry: x = −8 -------------- Which equation represents the axis of symmetry? 1. x = 3 3. x = 23 2. y = 3 4. y = 23 -------------- www.castlelearning.com/review/teacher/AssignmentPrinting.aspx 6/10 3/18/13 POW #16 - 2013 34. 35. The equation y = x 2 + 3x − 18 is graphed on the set of The equation y = −x 2 − 2x + 8 is graphed on the set of axes below. axes below. Based on this graph, what are the roots of the equation Based on this graph, what are the roots of the equation −x 2 − 2x + 8 = 0? x 2 + 3x − 18 = 0? 1. 8 and 0 3. 9 and −1 1. −3 and 6 3. 3 and −6 2. 2 and −4 4. 4 and −2 2. 0 and −18 4. 3 and −18 -------------- -------------- 36. Find algebraically the equation of the axis of symmetry and the coordinates of the vertex of the parabola whose equation is y = −2x 2 − 8x + 3. Equation of the AOS: x = Coordinates of the vertex: ( , ) -------------- www.castlelearning.com/review/teacher/AssignmentPrinting.aspx 7/10 3/18/13 POW #16 - 2013 37. 39. What is the equation of the axis of symmetry of the parabola shown in the diagram below? The height, y, of a ball tossed into the air can be represented by the equation y = −x 2 + 10x + 3, where x is the elapsed time. What is the equation of the axis of symmetry of this parabola? 1. y = 5 3. x = 5 2. y = −5 4. x = −5 -------------- 40. A student correctly graphed the parabola shown below to solve a given quadratic equation. 1. x = −0.5 2. x = 2 3. x = 4.5 4. x = 13 -------------- 38. If Ann correctly factors an expression that is the difference of two perfect squares, her factors could be: 1. 2. 3. 4. (2x + y)(x − 2y) (2x + 3y)(2x − 3y) (x − 4)(x − 4) (2y − 5)(y − 5) -------------- www.castlelearning.com/review/teacher/AssignmentPrinting.aspx What are the roots of the quadratic equation associated with this graph? 1. 2. 3. 4. −6 and 3 −6 and 0 −3 and 2 −2 and 3 -------------- 8/10 3/18/13 POW #16 - 2013 41. 45. The expression x 2 − 36y2 is equivalent to State the equation of the axis of symmetry and the coordinates of the vertex of the parabola graphed below. 1. 2. 3. 4. (x (x (x (x − 6y)(x − 6y) − 18y)(x − 18y) + 6y)(x − 6y) + 18y)(x − 18y) -------------- 42. What are the factors of the expression x 2 + x − 20? 1. 2. 3. 4. (x (x (x (x + 5) and (x + 5) and (x − 5) and (x − 5) and (x + 4) − 4) + 4) − 4) -------------- 43. 1. 2. 3. 4. AOS: x = 1; vertex (1, −5) AOS: y = 1; vertex (1, −5) AOS: x = 1; vertex (1, 5) AOS: x = 1; vertex (−1, −5) -------------- Which ordered pair is a solution of the system of equations y = x + 3 and y = x 2 − x? 1. (6,9) 3. (3,−1) 2. (3,6) 4. (2,5) -------------- 44. The area of a rectangle is represented by x 2 − 5x − 24. If the width of the rectangle is represented by x − 8, express the length of the rectangle as a binomial. 1. x – 3 3. x + 3 2. x – 16 4. x + 32 -------------- www.castlelearning.com/review/teacher/AssignmentPrinting.aspx 9/10 3/18/13 POW #16 - 2013 46. 48. What are the vertex and the axis of symmetry of the parabola shown in the graph below? The equation of the axis of symmetry of the graph y = 2x 2 – 3x + 7 is 1. x = 2. y = 3. x = 4. y = -------------- 1. 2. 3. 4. vertex: (1,6); axis of symmetry: y = 1 vertex: (1,6); axis of symmetry: x = 1 vertex: (6,1); axis of symmetry: y = 1 vertex: (6,1); axis of symmetry: x = 1 49. What is the vertex of the parabola represented by the equation y = –2x 2 + 24x – 100? -------------- 47. 1. x = –6 3. (6, –28) 2. x = 6 4. (–6, –316) -------------- Which expression is equivalent to 64 – x 2? 1. 2. 3. 4. (8 – x)(8 – x) (8 – x)(8 + x) (x – 8)(x – 8) (x – 8)(x + 8) -------------- 50. The graph of a parabola is represented by the equation y = ax 2 where a is a positive integer. If a is multiplied by 2, the new parabola will become 1. 2. 3. 4. narrower and open downward narrower and open upward wider and open downward wider and open upward -------------- www.castlelearning.com/review/teacher/AssignmentPrinting.aspx 10/10