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 #839065 by Edwin McCravy(20056) $\"\"$ $\"About$

You can put this solution on YOUR website!

\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "Put the base on the x-axis and the axis of symmetry on the y-axis\r\n" );
document.write( "and let each unit be 1 foot.  Then it has x-intercepts at (10,0) and \r\n" );
document.write( "(-10,0) and passes through the point (1,8).\r\n" );
document.write( "\r\n" );
document.write( "We could use the vertex form of a parabola, but since I don't know which\r\n" );
document.write( "vertex form you've studied, I'll use the general form:\r\n" );
document.write( "\r\n" );
document.write( "Its equation is \r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "Substitute the three points it passes through:\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "Simplify:\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "Subtract the third equation from the first equation and get\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "Then a = 8-c\r\n" );
document.write( "\r\n" );
document.write( "100a + c = 0\r\n" );
document.write( "100(8-c) + c = 0\r\n" );
document.write( "800-100c + c = 0\r\n" );
document.write( "800-99c = 0\r\n" );
document.write( "-99c = -800\r\n" );
document.write( "   c = 800/99 \r\n" );
document.write( "\r\n" );
document.write( "a = 8-c\r\n" );
document.write( "a = 8-800/99 = -8/99\r\n" );
document.write( "\r\n" );
document.write( "So the equation of the parabola is\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "So the height at the center is when x=0 or 800/99 or 8.08080808... feet.\r\n" );
document.write( "\r\n" );
document.write( "Edwin

\n" ); document.write( "

\n" );