posted by Hamza .
The Lions Gate bridge in Vancouver is a suspension bridge. The main span between the two towers, is 427m long. Large cables are attached to the ends of the both towers, 50m above the road. Each large cable forms a parabola. The road is suspended from the large cables by the series of shorter vertical cables. The shortest vertical cable measures 2m. Find the quadratic function that models one of the large cables?
Suppose we draw the cables on an x-y axis with the road as the x-axis.
and the posts at (-213.5,0) and (213.5,0) , with their tops at (-213.5,50) and (213.5, 50)
That would make (0,20) the vertex of the parabola
the equation using y = a(x-p)^2 + q , where (p,q) is the vertex, would be
y = a(x-0)^2 + 20
but (213.5, 0) lies on it
0 = a(213.5)^2 + 20
a = -20/213.5^2 = appr - .000439
a model equation could be
y = -.000439x^2 + 20
BTW, having crossed that bridge several times, I would have noticed that the suspended road is actually curved, and the cables are not a parabolas but rather a "Catenary"