SOLUTION: 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 cable

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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.
Answer by lwsshak3(11628) (Show Source):
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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.
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Standard form for parabola: y=A(x-h)^2+k, with (h,k) being the (x,y) coordinates of the vertex.
For given problem:
coordinates of vertex is at (0,0)
y=A(x-0)^2+0
y=Ax^2
Using point (300,150) to solve for A
150=A(300)^2
A=150/300^2=1/600
Equation:
y=x^2/600
see graph below as a visual check on the answer
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