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Warm Up

Warm Up. Order the following from widest to narrowest: y = -2x 2 , y = 5x 2 , y = .5x 2 , y = -3.5x 2 Find the vertex of y = -2x 2 – 8x – 10. Find the root(s) of y = 3x 2 + 5x – 1. Solve: 0 = -2x 2 – 8x – 10. Homework Solutions. Basketball parabola!.

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Warm Up

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  1. Warm Up • Order the following from widest to narrowest: y = -2x2, y = 5x2, y = .5x2, y = -3.5x2 • Find the vertex of y = -2x2 – 8x – 10. • Find the root(s) of y = 3x2 + 5x – 1. • Solve: 0 = -2x2 – 8x – 10.

  2. Homework Solutions

  3. Basketball parabola! • http://www.youtube.com/watch?v=dSRWY5vUHCU • Until 1:25

  4. Quadratic modeling • We can create quadratic functions to model real world situations all around us. • We can use these models to find out more information, such as: • Minimum/maximum height • Time it takes to reach the ground • Initial height

  5. Example #1: For a typical basketball shot, the ball’s height (in feet) will be a function of time in flight (in seconds), modeled by an equation such as h = -16t2 +40 t +6. a) What is the maximum height of the ball? How long does it take to reach the maximum height?

  6. To find maximum height: • Are we looking for x or for y? • Graph the function. Adjust xmin and xmax, then press ZOOM 0. • Find the vertex.

  7. Example #2: • The distance of a diver above the water h(t) (in feet) t seconds after diving off a platform is modeled by the equation h(t) = -16t2 +8t +30. a) How long does it take the diver to reach her maximum height after diving off the platform? What is her maximum height?

  8. Example #3: • The height, H metres, of a rocket t seconds after it is fired vertically upwards is given by h(t) = -50t2 + 80t. a) What is the highest point that the rocket reaches? When does it reach this point?

  9. Example #1: For a typical basketball shot, the ball’s height (in feet) will be a function of time in flight (in seconds), modeled by an equation such as h = -16t2 +40 t +6. b) When will the shot reach the height of the basket? (10 feet)

  10. To find a time given height… • Let y2 = given height. • Find the intersection of y1 and y2

  11. Example #2: • The distance of a diver above the water h(t) (in feet) t seconds after diving off a platform is modeled by the equation h(t) = -16t2 +8t +30. b) When will the diver reach a height of 2 feet?

  12. Example #3: • The height, H metres, of a rocket t seconds after it is fired vertically upwards is given by h(t) = -50t2 + 80t. c) At what time(s) is the rocket at a height or 25 m?

  13. Example #1: For a typical basketball shot, the ball’s height (in feet) will be a function of time in flight (in seconds), modeled by an equation such as h = -16t2 +40 t +6. c) When will the ball hit the floor if it missed the basket entirely?

  14. To find the time it takes it hit the ground… • This is asking us when does the height = 0? So what are we trying to do here? • Let y2 = 0. • Find the intersection of y1 and y2

  15. Example #2: • The distance of a diver above the water h(t) (in feet) t seconds after diving off a platform is modeled by the equation h(t) = -16t2 +8t +30. c) When will the diver hit the water?

  16. Example #3: • The height, H metres, of a rocket t seconds after it is fired vertically upwards is given by h(t) = -50t2 + 80t. c) When will the rocket hit the ground?

  17. Example #1: For a typical basketball shot, the ball’s height (in feet) will be a function of time in flight (in seconds), modeled by an equation such as h = -16t2 +40 t +6. d) What is the height of the ball when it leaves the player’s hands?

  18. To find the initial height… • Find the y-intercept!

  19. Example #2: • The distance of a diver above the water h(t) (in feet) t seconds after diving off a platform is modeled by the equation h(t) = -16t2 +8t +30. d) How high is the diving board?

  20. Example #3: • The height, H metres, of a rocket t seconds after it is fired vertically upwards is given by h(t) = -50t2 + 80t. c) What was the initial height of the rocket?

  21. Summarize

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