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MCR 3U0 Unit 3 Practice Test – Quadratic Functions Name: All answers should be left in simplified, reduced form unless you are told to round to a specific number of decimal places. Knowledge (Answers should be in exact values only) 1. Simplify the following rational expressions. 2. Determine the maximum or minimum value for and state the value of x for which this occurs. Use your own convenient way. 3. Determine the number of zeros for the following functions: 4. Determine the values of k for which the function has two zeros. 5. Determine the number of PoI of the following linear-quadratic system, then solve the system. Application 6. The height, h(t), of a baseball, in metres, at time t seconds after it is tossed out of a window is modelled by the function a) For how long will the ball stay 20 metres above the ground? (A diagram might help) b) A boy shoots at the baseball with a paintball gun. The trajectory of the paintball is given by the function . Will the paintball hit the baseball? If so, when? At what height will the baseball be? 7. 9. A building measuring 90 m by 60 m is to be built. A paved area of uniform width will surround the building. The paved area is to have an area of 9000m2. How wide is the paved area? (Include a diagram and round final answers to two decimal places!) 8. An engineer is designing a parabolic arch. The arch must be 15m high, and 6m wide at a height of 8m. Determine a quadratic function that satisfies these conditions. (Include a diagram with labelled coordinates, no decimals!) 9. Tickets to the prom are $50. Usually 400 students attend. The prom committee knows that for every $2 increase in the price of the ticket, 40 fewer students attend the prom. What ticket price will maximize the revenue?
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