2 towers of a suspension bridge are 1000 meters apart and are 160 meters high. The cable between 2 towers hangs in a shape of parabola, which at its lowest is 40meters above the road.

Question

A. Find the equation of the parabola, if we put a coordinate system so that the axis of the parabola is the y-axis and the road is on the x axis.
B. How high is the cable 100 meter from a tower?

Answer 1

clearly, the vertex of the parabola is at (0,40). That means the equation is
y = ax^2 + 40
So now all you have to do is find a. You have the point (500,160) so just plug that in and you can get a.

Once you have a, then you just need y(400).