Math

On the reality TV show Last Man Standing, a package is thrown from a plane to the ocean below. The contestants must swim to the package to receive the "free pass" located inside the package. The path that the package follows can be modelled by the quadratic function d(t)= -4.9t^2 + 10t + 1200, where d represents the distance, in meters, that the package travels and t is the time in seconds.
A.) How long will it take for the package to reach the water?
B.) Determine the domain and range of the function
If someone could please show me step by step how to do this, that would be awesome. Thanks in advance.

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  1. your function is modelled by a parabola which opens downwards.

    when the package reaches the water, h(t) = 0
    -4.9t^2 + 10t + 1200 = 0
    t = (-10 ± √23620)/-9.8
    = -14.662 or 16.7029

    We will reject the negative time, so
    it took appr 16.7 seconds for the package to reach the water

    for the domain , since we would only use numbers greater than zero
    0 ≤ t ≤ 16.7029

    for the range, we need the vertex,
    the t of the vertex = -10/-9.8 = 1.020408
    plug that into the function:
    h(1.020408) = -4.9(1.020408)^2 + 10(1.020408) + 1200
    = 1205.1 m

    range: 0 ≤ y ≤ 1205.1

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