Dome with a parabolic shape?

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This is my last question for today!! Usually I'm good at math, but I've been sick for over a year and am now finding it hard to concentrate. :P Here is the question:

The dome over a town hall has a parabolic shape. The dome measures 48 m across and rises 12 m at its centre.

a) Determine the quadratic equation that models the shape of the dome.

I already did this and here is my answer. Please correct me if I'm wrong. :)

First Zero: (0,0) x1 = 0

Second Zero: (48,0) x2 = 48

Determining the location of the axis of symmetry:

x1 + x2 / 2

= 0 + 48 / 2

= 48 / 2

= 24

Therefore, the location of the axis of symmetry is x = 24.

b) A vertical column needs to be attached to the dome at a point that is 4 m away from its rim. How tall is the dome at this point?

I tried solving this but got lost.

c) The dome sits on top of the town hall, which is 20 m high. How high does the column have to be, to reach from the floor to the dome?

I did not get to that one because I know I need information from the other two questions in order to solve this. :P

Thank-you so much!