How do you build a Parabolic dish?While it is difficult to build a parabolic shape with a large amount of precision (in the absence of expensive machinery), there are a few tricks which allow anyone to build a crude parabolic dish.
One method is to cut out a two dimensional parabolic shape from some rigid material and then use it to help you model some three dimensional shape (out of aluminum foil or chicken wire, for instance). The focus of the parabola y = ax^2 is located at the point (0,p) where p = 1/4a^2.
Although it is more difficult to implement, nature provides us with a far more accurate way of obtaining a parabolic shape. If a body of water is in a rotating container (and the liquid and the container are rotating together at the same speed), the surface of the water takes the shape of a near perfect parabolic shape. The focus of the parabolic shape depends on the rate of the rotation and also on the density of the liquid (if you were using something other than water). This approach is probably more interesting for those interested in the optics of parabolic shapes.