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Math Help - Quadratic Problem Help

  1. #1
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    Quadratic Problem Help

    Thanks for your help in advance, here's the problem:

    The path of a golf ball can be modeled by a quadratic equation. The path of a ball hit an angle of 10 degrees can be modeled by h=-0.002d^2+0.4d where h is the height in meters and d is the horizontal distance the ball travels in meters until it first hits the gorund.

    a) What is the maximum height reached by the ball?


    The answer is 20m, usually I would just sub in 0 for d to find h but in this case it's different. What should I do?
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  2. #2
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    Hello, andi01!

    The path of a golf ball can be modeled by a quadratic equation.
    The path of a ball hit an angle of 10 can be modeled by: h\:=\:-0.002d^2+0.4d
    where h is the height in meters and d is the horizontal distance.

    a) What is the maximum height reached by the ball?

    The answer is 20m.
    Usually I would just sub in 0 for d to find h. . . Why?
    Think of what you said . . .

    You let d = 0.
    The ball has not moved yet.
    What is its height?
    . . Obviously it's still on the ground!


    Here's one way of looking at it:

    The graph of h \:=\:-0.002d^2 + 0.4d is a down-opening parabola: \cap

    Its maximum is at its vertex.
    The vertex is at: . v \:=\:\frac{\text{-}b}{2a} \quad\Rightarrow\quad d \:=\:\frac{\text{-}0.4}{2(\text{-}0.002)} \:=\:100

    The maximum height is: . h \:=\:-0.002(100^2) + 0.4(100) \:=\:20 m.

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