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Name __________________________________ Date _________________ Period _________ Unit 6 Review – Quadratics Functions NON-CALCULATOR State the domain and range and determine if the relation is a function. 1. {(1, -4), (2, -3), (3, -4), (4, -3), (5, -4)} 2. {(0, 2), (1, -3), (0, -2), (2, 2)} Domain: ___________________ Domain: ____________________ Range: ____________________ Range: _____________________ Function: yes or no Function: yes or no 3. 4. Domain: ___________________ Domain: ___________________ Range: ____________________ Range: ____________________ Function: yes or no Function: yes or no 5. 6. Domain: ___________________ Domain: ___________________ Range: ____________________ Range: ____________________ Function: yes or no Function: yes or no Review Unit 6 Find the indicated value of f(x). 7. f(x) = 2x2 –x + 1; f(-2) = 8. f(x) = -3x - 8; f(3) = Analyze and graph the following quadratic functions. Include your Axis of Symmetry on the graph. 9. y = 3(x + 3)(x + 3) x y x y x y Vertex Axis of Symmetry Max or Min Value Domain: Range: Roots: *Vertex Form: _________________ 10. y = -2(x + 6)2 + 2 Vertex Axis of Symmetry Max or Min Value Domain: Range: Roots: *Root Form: ___________________ 11. y = -x2 + 4x + 5 Vertex Axis of Symmetry Max or Min Value Domain: Range: Roots: *Vertex Form: _________________ *Root Form: __________________ Use the following information to write an equation for the quadratic function. 12. roots: -4, 1 f(5) = 16 13. vertex: (-3, 1) f(4) = -13 14. Use root form Review Unit 6 15. Use vertex form f(1) = -4 f(2) = -5 Describe the following transformations on the function y = x2. 16. y = 2(x - 1) 2 17. y = -x2 - 4 18. y = -2(x + 3) 2 - 5 19. y = 2 (x - 7) 2 + 2 3 Write the equation for the function y = x2 with the following transformations. 20. shift right 4 and up 2 21. reflect across the x-axis, shift left 2 22. shrink by a factor of 1 , shift left 6 and up 3 2 1 24. If you wanted to shift y = - (x + 6) 2 – 2 up 4 2 and left 3, what would be the new equation? Review Unit 6 23. Reflect across the x-axis, stretch by a factor of 2, shift right 8 and down 4 25. If you wanted to shift y = 2x2 - 6 right 3 and up 7, what would be the new equation? Review. 26. Solve 5x² - 4x = 2 27. Solve 2x² + x = 15 28. Solve 6x – 3 + 3x = 24 29. Solve 2x² = 32 30. a) Find the equation of the line that contains the point ( -4, 4) and has the same y-intercept as 2x + 3y = 9 b) What is the equation of the line parallel to the line found in part a and has a y-intercept of -5. Review Unit 6 31. Ellie is landscaping her yard. She wants to buy bushes that cost $19 each and flowers that cost $6 each. Her budget allows her to spend no more than $200 on this landscaping project. Write an inequality that could be used to find how many bushes, b, and flowers, f, she could afford. 32. The cost of being a member of Macy’s Health and Fitness Club is an initial fee of $80 plus a monthly fee of $30. If Joe wants to join the club, how many months could he be a member if he has budgeted $470 for fees to a fitness club? 33. At a baseball game, Lynn spent $18.50 on 3 cotton candies and 5 soft drinks for her children. Another parent spent $17.00 on 6 cotton candies and 2 soft drinks. What is the price for 1 cotton candy and 1 soft drink? Answers 1. D: {1,2, 3, 4, 5} R: {-4, -3} YES 2. D: {0, 1, 2}; R: {-3, -2, 2} NO 3. D: {-3, 1, 2, 5, 6} R: {-2, 0, 2} YES 4. D: {-3, 0, 2, 4} R: {-3,-1,2,3,4} NO 5. D: –9 < x 8; R: –4 y 6; YES 6. D: x –6; R: All Real #’s; NO 7. 11 8. –17 9. Vertex: (-3, 0) Axis of Symmetry: x = -3 Min at y = 0 Domain: All Reals Range: y 0 Roots: -3 and -3… double root Points on Graph:(–4,3), (–3,0), (–2,3) *Vertex Form: y = 3(x + 3)2 10. Vertex: (-6, 2) Axis of Symmetry: x = -6 Max at y = 2 Domain: All Reals Range: y 2 Roots: -5 and -7 Points on Graph: (–8,–6),(-7,0), (-6,2),(-5,0),-4,-6) *Root Form: y = -2(x + 7)(x + 5) 11. Vertex: (2, 9) Axis of Symmetry: x = 2 Max at y = 9 Domain: All Reals Range: y 9 Roots: -1 and 5 Points on Graph: (0,5),(1,8), (2,9),(3,8),(4,5) *Vertex Form: y = –(x – 2)2 + 9 *Root Form: y = –(x + 1)(x + 5) 4 12. y = (x + 4)(x – 1) 9 2 13. y = (x + 3)2 + 1 7 14. y = (x + 1)(x – 3) 15. y = –(x + 1) 2 + 4 16. stretch by factor of 2, horizontal translation 1 unit to right 17. reflected across the x-axis, vertical translation 4 units down 18. reflected across the x-axis, stretch by factor of 2, horizontal translation 3 units to left, vertical translation 5 units down 19. shrink by factor of 2 , 3 horizontal translation 7 units to right, vertical translation 2 units up 20. y = (x – 4)2 + 2 21. y = -(x + 2)2 1 22. y = (x + 6)2 + 3 2 23. y = -2(x – 8) 2 – 4 24. y = - 1 (x + 9)2 + 2 2 25. y = 2(x – 3)2 + 1 26. 2 14 5 27. 5 , 3 2 28. 3 29. 4 1 x3 4 1 b) y = x 5 4 31. 19b + 6f < 200 32. 13 months 33. $4.50 for one of each 30. a) y =