document.write( "Question 253303: An arch is built so that it is 6 feet wide at the base. Its shape can be represented by a parabola with the equation y = -2x2 + 12x, where y is the height of the arch. The maximum height, y, of the arch is blank feet \n" ); document.write( "

Algebra.Com's Answer #185599 by Earlsdon(6294) $\"\"$ $\"About$

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$\"y+=+-2x%5E2%2B12x\"$
\n" ); document.write( "The maximum height of this parabola will be found at its vertex, so let's find out where the vertex is:
\n" ); document.write( "The x-coordinate of the vertex is given by:
\n" ); document.write( " $\"x+=+%28-b%29%2F2a\"$ where: a = -2 and b = 12, so...
\n" ); document.write( " $\"x+=+%28-12%29%2F2%28-2%29\"$
\n" ); document.write( " $\"x+=+12%2F4\"$
\n" ); document.write( " $\"x+=+3\"$ Now substitute this value of x into the original equation to find the y-coordinate of the vertex and, this of course, corresponds to the maximum height of the arch in your problem.
\n" ); document.write( " $\"y+=+-2x%5E2%2B12x\"$ Substitute x = 3.
\n" ); document.write( " $\"y+=+-2%283%29%5E2%2B12%283%29\"$
\n" ); document.write( " $\"y+=+-18%2B36\"$
\n" ); document.write( " $\"highlight%28y+=+18%29\"$ feet. This is the maximum height of the arch. \n" ); document.write( "

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