document.write( "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. \n" ); document.write( "

Algebra.Com's Answer #672238 by ikleyn(52803) $\"\"$ $\"About$

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\n" ); document.write( "Students noticed that the path of water from a water fountain seemed to form a parabolic arc.
\n" ); document.write( "They set a flat surface at the level of the water spout and measured the maximum height of the water from the flat surface
\n" ); document.write( "as 5 inches and the distance from the spout to where the water hit the flat surface as 8 inches.
\n" ); document.write( "Construct a function model for the stream of water.
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document.write( "The observation facts are:\r\n" );
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document.write( "    We have a parabola open downward.\r\n" );
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document.write( "    The zeroes (the x-intercepts) are these points: (0,0) and (8,0).\r\n" );
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document.write( "    The maximum (the vertex) is at the point (4,5).\r\n" );
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document.write( "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).\r\n" );
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document.write( "The fact that x=0 is the root implies\r\n" );
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document.write( "-a*(0-4)^2 + 5 = 0,  or\r\n" );
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document.write( "-16a = -5,  or\r\n" );
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document.write( "a = .\r\n" );
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document.write( "Thus the parabola is  y = .\r\n" );
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document.write( "You may further simplify (or transform) this equation as you want.\r\n" );
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