Advanced Math Quadratics Review Name: Dec. 2016
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1 Advanced Math Quadratics Review Name: Dec Graph the given quadratic by finding the vertex and building a table around it. Identify the axis of symmetry, maximum or minimum value, domain and range (both in interval notation). 1. ( ) axis of symmetry: vertex: max or min: domain: range: 2. ( ) axis of symmetry: vertex: max or min: domain: range: 3. ( ) axis of symmetry: vertex: max or min: domain: range:
2 Graph the given quadratic by finding the vertex and building a table around it. Identify the axis of symmetry, maximum or minimum value, domain and range (both in interval notation). 4. ( ) axis of symmetry: vertex: max or min: domain: range: Find the VERTEX of the quadratic equation that is given in vertex form. Also, state the value of graph opens up or down. and tell whether the 5. ( ) 6. ( ) 5.) vertex = 5.) = opens: 6.) vertex = 6.) = opens: 7. ( ) 8. ( ) 7.) vertex = 7.) = opens: 8.) vertex = 8.) = opens: Graph the given quadratic by finding the vertex and building a table around it. Identify the axis of symmetry, maximum or minimum value, domain and range (both in interval notation). 9. ( ) vertex: axis of symmetry: max or min: domain: range:
3 Graph the given quadratic by finding the vertex and building a table around it. Identify the axis of symmetry, maximum or minimum value, domain and range (both in interval notation). 10. ( ) vertex: axis of symmetry: max or min: domain: range: 11. ( ) vertex: axis of symmetry: max or min: domain: range: 12. ( ) vertex: axis of symmetry: max or min: domain: range:
4 When : Use the method of completing the square to find the vertex form of the quadratic function. Identify the vertex and axis of symmetry. Does the quadratic have a max or a min? What is the max or min? Lastly, identify the domain and range (in interval notation). 13. vertex form: vertex: axis of symmetry: max or min: domain: range: 14. vertex form: vertex: axis of symmetry: max or min: domain: range: 15. vertex form: vertex: axis of symmetry: max or min: domain: range: 16. vertex form: vertex: axis of symmetry: max or min: domain: range:
5 When : Use to find the -coordinate of the vertex. Then plug that value back into the equation to find the -coordinate of the vertex. What you have found is ( ). Lastly, identify the value for, and put the equation into vertex form. For #5 and #6, also find the axis of symmetry, max/min, domain and range(in interval notation). 17. vertex: opens: vertex form: axis of sym: max or min: domain: range: 18. vertex: opens: vertex form: axis of sym: max or min: domain: range: Match each equation with its graph. 19. ( ) 20. ( ) 21. ( ) 22. ( ) 23. ( ) 24. ( ) A B C D E F G H
6 Identify the equation of the given graph. There are NO vertical stretches or shrinks in #27-# or Match each equation with its graph. 31. ( ) 32. ( ) ( ) 35. ( ) 36. A B C D E F
7 Describe all transformations shown in the given equation. 37. ( ) ( ) 40. ( ) 41. ( ) 42. ( ) Sketch the quadratic using transformations. There are NO vertical stretches or shrinks in #43-#50. or 43. ( ) 44. ( ) 45. ( ) 46. ( )
8 Sketch the quadratic using transformations. There are NO vertical stretches or shrinks in #43-#50. or 47. ( ) ( ) Find the maximum or minimum value of the function. State whether this value is a max or a min. 51. ( ) 52. ( ) Max / Min: (Circle one) Max / Min: (Circle one) 53. ( ) 54. ( ) Max / Min: (Circle one) Max / Min: (Circle one)
9 For the following problems, answer the given questions. Pick ONE of the graphs in each problem to show the max or min value. 55. The path of a tennis ball during a serve is given by ( ) where ( ) is the height of the tennis ball (in feet) at time (in seconds). a. When is the tennis ball at its maximum height? 55a.) Hint: What are you really finding here? b. What is the maximum height of the tennis ball? 55b.) Hint: What are you really finding here? 56. A ball is thrown upward with an initial velocity of feet per second. The height in feet of the ball seconds after it is released is given by the equation ( ). What is the maximum height of the ball? 56.) 1. vertex: ( ); axis of symmetry: ; min value: ; domain: ( ); range: [ ) 2. vertex: ( ); axis of symmetry: ; min value: ; domain: ( ); range: [ ) 3. vertex: ( ); axis of symmetry: ; max value: ; domain: ( ); range: ( ] 4. vertex: ( ); axis of symmetry: ; max value: ; domain: ( ); range: ( ] 5. vertex = ( ); ; opens DOWN 6. vertex = ( ); ; opens DOWN 7. vertex = ( ); ; opens UP 8. vertex = ( ); ; opens UP 9. vertex = ( ); axis of symmetry: ; min: ; domain: ( ); range: [ ) 10. vertex = ( ); axis of symmetry: ; min: ; domain: ( ); range: [ ) 11. vertex = ( ); axis of symmetry: ; max: ; domain: ( ); range: ( ] 12. vertex = ( ); axis of symmetry: ; max: ; domain: ( ); range: ( ]
10 13. ( ) ; vertex: ( ); axis of symmetry: ; min value: ; domain: ( ); range: [ ) 14. ( ) ; vertex: ( ); axis of symmetry: ; min value: ; domain: ( ); range: [ ) 15. ( ) ; vertex: ( ); axis of symmetry: ; min value: ; domain: ( ); range: [ ) 16. ( ) ; vertex: ( ); axis of symmetry: ; min value: 10; domain: ( ); range: [ ) 17. ( ) ; vertex: ( ); axis of symmetry: ; max value: ; domain: ( ); range: ( ] 18. ( ) ; vertex: ( ); axis of symmetry: ; max value: ; domain: ( ); range: ( ] 19. D 20. C 21. E 22. G 23. B 24. A 25. H 26. F 27. ( ) 28. ( ) 29. ( ) C 32. A 33. D 34. E 35. F 36. B 37. Shift units to the right, Shift units up 38. Reflection over the -axis, Shift units up 39. Shift units to the left, Vertical Stretch of, Reflection over the -axis, Shift units down 40. Shift unit to the left, Vertical Stretch of, Shift units down 41. Shift units to the right, Vertical Shrink of 42. Shift units to the left, Reflection over the -axis, Shift units down 43. vertex: ( ); opens: down 44. vertex: ( ); opens: down 45. vertex: ( ); opens: up 46. vertex: ( ); opens: down 47. vertex: ( ); opens: down 48. vertex: ( ); opens: up 49. vertex: ( ); opens: down 50. vertex: ( ); opens: up 51. Max: 52. Max: 53. Min: 54. Min: 55a. seconds 55b. feet 56. feet
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