But since is two horizontal units to the left of the vertex, the independent variable value two horizontal units to the right of the vertex must produce the same function value by symmetry. Therefore the function must pass through , which, by the logic illustrated above leads us to the conclusion that:
Now that you have a system of three linear equations in three variables, solve the system to derive the required coefficients:
I use the MDETERM function in Excel to solve such systems, but there are lots of linear system solvers on the web. Or solve it yourself -- the coefficients are all integers.
My calculator said it, I believe it, that settles it