9:25 PM Sun Jul 24 . . . @ 12% % TOD O + : 9 6. Determine the vertex of the function y = -3(x - 1)2 - 2. 7. Determine the solution(s) to the quadratic equation x2 + 2x - 8 = 0 Page 2 Determine the solution(s) to the quadratic equation 5x2 - 30x + 45 = 0 9. Determine the root(s) of the quadratic equation 7x2 - 7 = 0. 10. Express the solution to the quadratic equation 9x2 - 12x + 2 = 0 in simplest form. 11. The path of a diver under water after a dive is in the shape of a parabola that opens upward. Using the water surface as the x-axis, the x-intercepts that the diver makes are I'm and 5 m from the edge of the pool. The maximum depth, d, in metres, of the diver under water is 2 m. Which quadratic equation models the path of the diver? D I W d = - (x-1)(x-5) C. d= - - ( x+1)(x+5 ) b. d = = (x- 1)(x - 5) d. d = 4 (x+ 1)(x+ 5 ) V Page 39:25 PM Sun Jul 24 . . . @ 12% % TOD O + a. d= -= (x-1)(x-5) C. d = -= (x+ 1)(x+ 5) b. d= = (x- 1)(x- 5) =(x+ 1)(x+5) Page 3 12. Which is the equation for the family of quadratic functions with x-intercepts 3 and -2? 13. The roots of the equation of a quadratic function are x = 3 and x = 5. Find an equation for the quadratic function that contains the point (1, -24). Part B: Solving Problems Each question is worth 5 marks: 4 marks for the answer support choice and I mark for the correct answer. 14. a) Determine the vertex of the function f(x) = -2x2 + 8x -6 by completing the square. b) Is the vertex found in part a) a minimum or a maximum? Explain. 15. The height, h, in metres, of an object t seconds after it is thrown into the air is given by h() = -4.9:2 + 341+ 5. What is the maximum height of the object, to the nearest metre V Page 49:25 PM Sun Jul 24 . . . @ 12% % 5 TOD O + : 9 MHF4U Lesson 11 Assignment In this assignment you are going to explore the characteristics quadratic functions. Make sure you answer all questions in the spaces provided Part A: Finding the Answer In this section, you are going to explore characteristics of quadratic functions.. In the textbox provide your answer and give your proof from the equation to support your answer. Each question is worth 2 marks: 2 marks for the answer support choice and I mark for the correct answer. Identify the choice that best completes the statement or answers the question. Multiple Choice Identify the choice that best completes the statement or answers the question. 1. Determine the domain of the function y = (x -4)2 + 8. 2. Determine the range of the function y = (x -4)2 + 8. 3. Which of these quadratic functions does NOT have a minimum value? a. y = (x-4)2 - 8 C. y= -x2 + 4x +2 b. y = 3x2 - 6x + 5 y = 4(x - 2)(x+ 1) Page 1 4. Which of these quadratic functions has a maximum value? a. y = 3x2 - 3x + 5 C. y = 3(x - 2)2 + 5 b. y = (3-x)2 d. y=-2(4-x)2+1 DI - 5. Determine the vertex of the function y = -2x2 - 20x - 51 V