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Quadratic Functions Review: Level 1 + 2 Questions 1. Determine the domain and range for each of the following relations. (a) {(-1,-6), (0,-6), (1, -6), (2, -6)} (b) {(5, 4), (4,3), (4,7), (2, -1)} (c) (d) y y O O x x 2. Which of the relations given in #1 are functions? 3. Complete the table. Equation vertex equation for axis of symmetry range x=2 {y| y ≥ -4, y ε R} Max/Min and its value a) y x 2 1 b) y 5x 2 2 c) y 2x 3 4 d) 4. Write an equation for a quadratic function which is congruent to y = 3x2 and has a minimum value of 6 when x = -5. (congruent means the same size and shape) 5. Use finite differences to determine whether each function is linear, quadratic or neither. a) x y -2 4 -1 5 0 8 1 13 2 20 b) x -2 -1 0 1 2 y 13 16 19 22 25 6. Complete the square of y 2 x 2 4 x 1 7. Graph y = - 2( x 2) 2 + 3 showing the vertex and 4 other points. Level 3 Questions 8. Determine the equation of a quadratic function with a maximum value of 5 when x = - 2, and passing through the point (2, -10). 9. A football is kicked straight up in the air. Its height above the ground is approximated by the relation h 25t 5t 2 , where h is the height (m) and t is the time (s). a. What is the maximum height reached by the football? b. After how many seconds does this occur? 10. Phyllis wants to make the largest possible rectangular vegetable garden using 18m of fencing. The garden is right behind the back of her house, so she has to fence it on only 3 sides. Determine the dimensions that maximize the area of the garden. 11. Max sells an average of 280 CDs a day at $20 each. For every $0.50 increase in unit price, daily sales will drop by five units. a. What unit price will maximize Max’s daily revenue? b. What is the maximum revenue? 12. A glassworks company has a daily production cost (C) in $ given by C 0.2b 2 10b 650 , where b is the number of crystal bowls made. a. How many bowls should be made to minimize the production cost? b. What is the cost when this many bowls are made? 13. A long jumper reaches a maximum height of 0.735 metres before landing 7.000 metres from where she started her jump. Assume that her trajectory is parabolic. Determine a realistic equation of the parabola that models the trajectory. Level 4 Questions 14. The side length of a square is 10cm. Four points on the square are joined to form an inner square, as shown. a) Find the minimum area of the inner square, in square centimetres b) Describe how you could find the minimum area of the inner square for any side length of the outer square. 15. A parabolic bridge over a road is 4 metres tall, 4 metres wide at the base, and 15 metres long. Determine the maximum height of a 2 metres wide truck that can drive under the bridge. Explain and justify your reasoning. Answers: 1a) {x=-1,0,1,2}, {y=-6} b) {x=2,4,5}, {y=-1,3,4,7} c) x x 3, x , y y d) x 4 x 4, x , y 2 y 1, y 2.a,d 3. a) (0,-1), x=0, y y 1, y , min of -1 b) (2,0), x=2, y y 0, y , max of 0 c) (-3,4), x=-3, y y 4, y , max of 4 d) y ( x 2) 2 4 , (2,-4), min of -4 4. y 3( x 5) 2 6 5.a)quadratic b) linear 6. y 2( x 1) 2 1 8. y 15 ( x 2)2 5 16 9a)31.25m b)2.5sec 10. 9m x 4.5m 11a)$24 b)$5760 12a)25 bowls b)$525 13. h 0.06(d 3.5)2 0.735 14a)50cm b) side length squared and divided by two 15. just below 3m to allow for clearance of the truck