Unit5Workbook.doc

# S this is the or c when does the soccer ball reach

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______ s (This is the _________________ or __________ ) c) When does the soccer ball reach its maximum height? ______ s (This is the ________________________ or ___-value of vertex) d) What is the soccer ball’s maximum height? ______ m (This is the ______________________ or ___-value of vertex) e) What is the soccer ball’s height at 1 s? ______ m (This is the ____-value of a _____________ on the graph) f) When does the soccer ball reach 48 m? ______ s and ______ s (These are the ____-values of ______________ on the graph) g) Why do we only use positive values of h and t ? 5 - 8

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MFM 2P Date: ________________________ Unit 5: Quadratic Relations Example 2. Kyle and Tim built a model rocket that is equipped with a motion detector that measures the height of the rocket at various times. The height, h , of the rocket in metres , after t seconds , is given by 80 30 5 2 t t h . Kyle and Tim climb to the roof of a building to launch their model rocket. Tim launched the rocket and Kyle laughed, “This is just like those quadratic problems we learned about in math class!” a) How tall is the building? b) At what time does the model rocket hit the ground? c) When does the model rocket reach its maximum height? d) What is the model rocket’s maximum height? e) What is the model rocket’s height at 2 s? f) What time is it when the rocket is 45 m in the air? Example 3. A helium-filled balloon is released by Katrina, and follows a parabolic path due to the wind. It rises up in the air, but once it begins deflating it travels back down to the ground. The height of the balloon h , in feet, with respect to time t , in minutes, is represented by: h = –3.75t 2 – 29.625t +3 , and its graph is displayed below. a) After how long does the balloon land on the ground? b) What is the height of the balloon at 3 min? c) What is the maximum height reached by the balloon? d) When does the balloon begin deflating? *e) How tall is the Katrina? 5 - 9 Be sure to include appropriate units of measurement . They will be given in the question, or you could find them on the appropriate axes.
MFM 2P Date: ________________________ Unit 5: Quadratic Relations 5.3 Applications of Quadratic Functions PRACTICE 1. The height, h , in metres, of an infield fly ball, t seconds after being hit is given by the equation t t h 30 5 2 ; its graphs is provided below. a) Determine the height of the ball at 5 seconds. b) Determine the height of the ball at 2 seconds. c) State the maximum height of the ball. d) Determine the x-intercepts. e) For how long is the ball in the air? e) State the equation of the axis of symmetry. f) When does the ball reach its maximum height? *g) For how long was the ball above 40 m ? 2. Tyson kicks a football into the air. The height of the ball, h , in metres, after t seconds, is represented by the equation t t h 20 5 2 ; its graph is provided below.
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