equation of a parabola arch

Question

a)find the equation of the parabolic arch curve.
b)how far from the center of the arc would you need to be in order for the height of the arc to be 15 meters.link to the image
https://i.stack.imgur.com/aktsu.jpg
I don't know how to proceed in this, should I convert it into coordinates and then proceed, but the proper axis are not given so where should the vertex be?

Answer 1

Hint: Identify the $\;y\,-$ axis with the parabola axis of symmetry and decide that the parabola vanishes at the points $\;(-8.5,0)\,,\,\,(8.5,0)\;$ . Thus your parabola is

$$y=a(x-8.5)(x+8.5) $$

Finally, observe the parabola's vertex is at $\;(0,24)\;$ ...