A hot air balloon takes off from the edge of a plateau. Impose a coordinate system as pictured below and assume that the

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A hot air balloon takes off from the edge of a plateau. Impose a
coordinate system as pictured below and assume that the path the
balloon follows is the graph of the quadratic function 𝑓(𝑥) = −2𝑥 2
+ 12𝑥 The land drops at a constant incline from the plateau at the
rate of 1 vertical foot for each 2 horizontal feet. Answer the
following questions:
(a) Find a linear function 𝑔(𝑥) that describes how much the
ground inclines, where x is the distance from the takeoff. (b) What
is the maximum height of the balloon above plateau level? (c) What
is the maximum height of the balloon above ground level? (d) Where
does the balloon land on the ground?