document.write( "Question 289507: The shape of a supporting arch can be modeled by h(x) = -0.03x^2 + 3x,where h(x) represents the height of the arch and x represents the horizontal distance from one end of the base of the arch in meters. Find the maximum height of the arch. \n" ); document.write( "

Algebra.Com's Answer #209697 by Earlsdon(6294) $\"\"$ $\"About$

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The shape of the arch is that of a parabola (opening downward, of course)
\n" ); document.write( "The x-coordinate of maximum height of a parabola (the vertex) is given by:
\n" ); document.write( " $\"x+=+-b%2F2a\"$ where the a and b come from the standard form for a parabola: $\"ax%5E2%2Bbx%2Bc+=+0\"$ Here, the given equation is: $\"h%28x%29+=+-0.03x%5E2%2B3x\"$ , so a = -0.03 and b = 3
\n" ); document.write( "Making the appropriate substitutions, we get:
\n" ); document.write( " $\"x+=+-3%2F2%28-0.03%29\"$
\n" ); document.write( " $\"x+=+50\"$ Now substitute this into the given equation to find the maximum height at x = 50m.:
\n" ); document.write( " $\"h%2850%29+=+-0.03%2850%29%5E2%2B3%2850%29\"$
\n" ); document.write( " $\"h%2850%29+=+-0.03%282500%29%2B150\"$
\n" ); document.write( " $\"h%2850%29+=+-75%2B150\"$
\n" ); document.write( " $\"highlight%28h%2850%29+=+75%29\"$ meters. This is the maximum height of the arch. \n" ); document.write( "

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