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Math Help - A rocket is launced upward..

  1. #1
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    A rocket is launced upward..

    A rocket is launched upward from the top of a 30-foot tall platform. The height of the rocket in feet, h(t), at time t\geq0, is given by the equation h(t)= -16t^2+256t+30

    a) At what time is the rocket at a maximum height?

    b) What is the maximum height in feet that the rocket can reach?

    Can you show me how to do these?
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  2. #2
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    This problem is really asking about the coordinates of the vertex. The x-coordinate of the vertex represents time (t) and the y-coordinate represents height (h).

    To find the x-coordinate of the vertex of a quadratic of the form y=ax^2 + bx + c, use:

    x=- \frac{b}{2a}.

    Once you've found the x-coordinate, that represents the time at which the object reaches its highest point. To find the height AT THAT TIME, simply plug in the x-coordinate to your equation (for t) and you'll get out the height.
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