The suspension bridge cables are in the shape of a parabola. The

distance between two towers supporting the cable are 800 feet apart
and the height is 200 feet. If the vertical support cables are at 100 feet
intervals along the level roadway, what are the lengths of these vertical
cables?

1 answer

If the vertex is at (0,0) then you have said that y(400)=200
y = ax^2
a(400)^2 = 200
a = 200/160000 = 1/800
y = 1/800 x^2
So now find y at x=100,200,300
The curve is symmetric, so negative values of x produce the same results.