Y = X^2/(4*focal)
The old camera flash bulbs appeared to use a short focal length when compared to its radius. When the focal is 0.25, then Y will be unity when X is unity.
The web page to do this is only a text file. Feel free to save it as source on you computer.
The plots are 700x700 bitmaps which avoid the auto scaling features found in most plotting resources. The plot will define a segment shape from a input a focal length which is relative to the parabola's radius. By importing these plots into a graphic application for scaling, it should be possible to construct any type of parabola desired.