document.write( "Question 462493: In a suspension bridge the shape of the suspension cables is parabolic. The bridge shown in the figure has towers that are 600 m apart and the lowest point of the suspension cables is 150 m below the top of the towers. Find the equation of the parabolic part of the cables by placing the origin of the coordinate system at the vertex. \n" ); document.write( "

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In a suspension bridge the shape of the suspension cables is parabolic. The bridge shown in the figure has towers that are 600 m apart and the lowest point of the suspension cables is 150 m below the top of the towers. Find the equation of the parabolic part of the cables by placing the origin of the coordinate system at the vertex.
\n" ); document.write( "...
\n" ); document.write( "Standard form for parabola: y=A(x-h)^2+k, with (h,k) being the (x,y) coordinates of the vertex.
\n" ); document.write( "For given problem:
\n" ); document.write( "coordinates of vertex is at (0,0)
\n" ); document.write( "y=A(x-0)^2+0
\n" ); document.write( "y=Ax^2
\n" ); document.write( "Using point (300,150) to solve for A
\n" ); document.write( "150=A(300)^2
\n" ); document.write( "A=150/300^2=1/600
\n" ); document.write( "Equation:
\n" ); document.write( "y=x^2/600
\n" ); document.write( "see graph below as a visual check on the answer
\n" ); document.write( "..
\n" ); document.write( " $\"+graph%28+400%2C+400%2C+-500%2C+500%2C+-500%2C+500%2C+x%5E2%2F600%29+\"$ \n" ); document.write( "

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