document.write( "Question 1136732: The curve of the tunnel is represented by the equation y= - x^2+3.The width of the road is 7m. Calculate the maximum height, in m,of the tunnel. \n" ); document.write( "

Algebra.Com's Answer #754536 by ikleyn(52787) $\"\"$ $\"About$

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document.write( "The shape of the tunnel is represented by the downward parabola equation\r\n" );
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document.write( "    y = -x^2 +3.\r\n" );
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document.write( "The parabola has a vertex at elevation y=  = 3.\r\n" );
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document.write( "First, we need to determine the bottom elevation of the tunnel  y, where x = 7/2 = 3.5 m.\r\n" );
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document.write( "It is easy to do:   = -(3.5)^2 + 3 = -12.25 + 3 = -9.25 m.\r\n" );
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document.write( "Now, the height of the tunnel is the difference of two elevations \r\n" );
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document.write( "    H =  -  = 3 - (-9.25) = 12.25 m.     ANSWER\r\n" );
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