SOLUTION: Students noticed that the path of water from a water fountain seemed to form a parabolic arc. They set a flat surface at the level of the water spout and measured the maximum heigh

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Question 1057139: Students noticed that the path of water from a water fountain seemed to form a parabolic arc. They set a flat surface at the level of the water spout and measured the maximum height of the water from the flat surface as 5 inches and the distance from the spout to where the water hit the flat surface as 8 inches. Construct a function model for the stream of water.
Answer by ikleyn(52903) (Show Source):
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Students noticed that the path of water from a water fountain seemed to form a parabolic arc.
They set a flat surface at the level of the water spout and measured the maximum height of the water from the flat surface
as 5 inches and the distance from the spout to where the water hit the flat surface as 8 inches.
Construct a function model for the stream of water.
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The observation facts are: We have a parabola open downward. The zeroes (the x-intercepts) are these points: (0,0) and (8,0). The maximum (the vertex) is at the point (4,5). From this info, the parabola is y = -a(x-4)^2 + 5 with some positive coefficient "a". (The symmetry line is x=4 and the maximum is 5). The fact that x=0 is the root implies -a*(0-4)^2 + 5 = 0, or -16a = -5, or a = . Thus the parabola is y = . You may further simplify (or transform) this equation as you want.