document.write( "Question 1175726: An arch is in the shape of a parabola. It has a span of 208 meters and a maximum height of 26 meters.\r
\n" ); document.write( "\n" ); document.write( "Find the equation of the parabola (assuming the origin is halfway between the arch's feet).\r
\n" ); document.write( "\n" ); document.write( "Determine the height of the arch 55 meters from the center.
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Algebra.Com's Answer #801426 by ikleyn(52788) $\"\"$ $\"About$

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\n" ); document.write( "An arch is in the shape of a parabola. It has a span of 208 meters and a maximum height of 26 meters.\r
\n" ); document.write( "\n" ); document.write( "Find the equation of the parabola (assuming the origin is halfway between the arch's feet).\r
\n" ); document.write( "\n" ); document.write( "Determine the height of the arch 55 meters from the center.
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\n" ); document.write( "\n" ); document.write( " The solution by @ewatrrr is INCORRECT.\r
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document.write( "You have this instruction to place the origin at halfway between the arch's feet).\r\n" );
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document.write( "It means that the parabola is open downward and its vertex is at the point  (0,26),\r\n" );
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document.write( "while the x-intercepts are 104 =  meters away from the origin.\r\n" );
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document.write( "THEREFORE, you write the equation of the parabola in the form\r\n" );
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document.write( "    y(x) = -ax^2 + 26\r\n" );
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document.write( "and you find then the value of the coefficient \"a\" from the condition  y(104) = 0, which is\r\n" );
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document.write( "    -a*104^2 + 26 = 0,   or\r\n" );
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document.write( "     a =  =  = .\r\n" );
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document.write( "So, the parabola equation is  \r\n" );
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document.write( "    y(x) = -  + 26      ANSWER\r\n" );
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document.write( "CHECK.   y(0) = 26;    y(104) = -  + 26 = -  + 26 = -26 + 26 = 0.    ! Correct !\r\n" );
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document.write( "                                   y(x) = -  + 26\r\n" );
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document.write( "55 meters from the center, the height of the arch is\r\n" );
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document.write( "          y(55) = -  + 26 = 18.73 meters (rounded).\r\n" );
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\n" ); document.write( "\n" ); document.write( "Solved (correctly).\r
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