document.write( "Question 1203474: Bridge shaped like a parabolic arch has a horizontal distance of 20 feet. The height of a point 1 foot from the center is 8 feet. What is the maximum height of the bridge if it is located at the center? \n" ); document.write( "

Algebra.Com's Answer #839069 by ikleyn(52787) $\"\"$ $\"About$

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\n" ); document.write( "Bridge shaped like a parabolic arch has a horizontal distance of 20 feet.
\n" ); document.write( "The height of a point 1 foot from the center is 8 feet.
\n" ); document.write( "What is the maximum height of the bridge if it is located at the center?
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document.write( "Let x-axis be horizontal at the ground level, with the origin under the upper \r\n" );
document.write( "point of the bridge; y-axis vertical.\r\n" );
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document.write( "Then the parabola has x-intercepts at x= -10 ft and x= 10 ft.\r\n" );
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document.write( "So, the parabola has the form  y = a*(x-(-10))*(x-10) = a*(x+10)*(x-10) = a*(x^2-100).\r\n" );
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document.write( "Coefficient \"a\" is some real negative number (since the parabola is opened downward).\r\n" );
document.write( "We do not know this number. It is the only unknown in this problem,\r\n" );
document.write( "and our goal is to find this single unknown.\r\n" );
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document.write( "To find \"a\", use the fact that at x= 1 ft we have y= 8 ft, from the problem.\r\n" );
document.write( "It gives you this equation\r\n" );
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document.write( "    8 = a*(1^2 - 100),  or  8 = -99a,  which implies  a =  = -0.08080808...\r\n" );
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document.write( "Thus the quadratic function is y = ,\r\n" );
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document.write( "and it has the maximum at x= 0  (at the axis of symmetry).\r\n" );
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document.write( "Thus the maximum height of the bridge is   =  = 8.08080808... ft, \r\n" );
document.write( "or, after rounding, about 8.08 ft.    ANSWER\r\n" );
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