Problem

12 parabolas

Given that two of the parabolas have the equations \[y = x^2 - 12x + 27\] and \[y = -x^2 + 12x - 36,\] can you find the equations of the other parabolas?


You might like to design your own pattern of parabolas, perhaps using Desmos. You could start from our design, if you like.