Algebra

A toy rocket that is shot in the air with an upward velocity of 48 feet per second can be modeled by the function f(t)=-16t^2+48t , where t is the time in seconds since the rocket was shot and f(t) is the rocket’s height. What is the maximum height the rocket reaches?

16ft
36ft
48ft
or 144 ft

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  1. Well, that is a parabola. Where is the vertex?

    -16 t^2 + 48 t = h

    16 t^2 - 48 t = -h

    t^2 - 3 t = -(1/16)h

    t^2 - 3 t + 9/4 = -(1/16)h + 9/4

    (t - 3/2)^2 = -(1/16)(h - 36)

    ah ha, hits the vertex at the top when t = 1.5 seconds and h = 36 feet

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  2. thanks!!

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  3. You are welcome.

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