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Warm Up 1. Order the following from widest to narrowest: y = -2x 2, y = 5x 2, y =.5x 2, y = -3.5x 2 2. Find the vertex of y = -2x 2 – 8x – 10. 3. Find the root(s) of y = 3x 2 + 5x – 1. 4. Solve: 0 = -2x 2 – 8x – 10.

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Homework Solutions

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Basketball parabola! http://www.youtube.com/watch?v=dSRW Y5vUHCU http://www.youtube.com/watch?v=dSRW Y5vUHCU Until 1:25

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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

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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 = -16t 2 +40 t +6. a) What is the maximum height of the ball? How long does it take to reach the maximum height?

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

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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) = -16t 2 +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?

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Example #3: The height, H metres, of a rocket t seconds after it is fired vertically upwards is given by h(t) = -50t 2 + 80t. a) What is the highest point that the rocket reaches? When does it reach this point?

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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 = -16t 2 +40 t +6. b) When will the shot reach the height of the basket? (10 feet)

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To find a time given height… Let y 2 = given height. Find the intersection of y 1 and y 2

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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) = -16t 2 +8t +30. b) When will the diver reach a height of 2 feet?

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Example #3: The height, H metres, of a rocket t seconds after it is fired vertically upwards is given by h(t) = -50t 2 + 80t. c) At what time(s) is the rocket at a height or 25 m?

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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 = -16t 2 +40 t +6. c) When will the ball hit the floor if it missed the basket entirely?

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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 y 2 = 0. Find the intersection of y 1 and y 2

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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) = -16t 2 +8t +30. c) When will the diver hit the water?

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Example #3: The height, H metres, of a rocket t seconds after it is fired vertically upwards is given by h(t) = -50t 2 + 80t. c) When will the rocket hit the ground?

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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 = -16t 2 +40 t +6. d) What is the height of the ball when it leaves the player’s hands?

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To find the initial height… Find the y-intercept!

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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) = -16t 2 +8t +30. d) How high is the diving board?

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Example #3: The height, H metres, of a rocket t seconds after it is fired vertically upwards is given by h(t) = -50t 2 + 80t. c) What was the initial height of the rocket?

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