Birthday polynomials!

I posted last week about “birthday triangles” (in short, turn your birthdate of November 23, 1972 into a triangle with coordinates (1,1) (2,3) (7,2) – or a quadrilateral by including (1,9) – and then perform coordinate geometry or transformational geometry tasks using them.)

Sam, in the comments, suggested using birthdays to create polynomials. Cool. (How will this work?)

And then I remembered “family curves”

Express a birthday (yours, your mom’s, doesn’t matter who) as three coordinates: (1,1), (2,3), (7,2) – and write the equation of the parabola that passes through these three points. I used this as an early transition to polynomial functions last time I taught precalculus. It was also probably the only time the kiddies saw a system of 3 equations, 3 unkowns, before college

I’ll leave it to commenters to solve. Or solve your own. Or discuss which birthdays don’t make vertically oriented parabolas (parabolae?) or any parabola/s/e at all.

Edit – a friend points out that a (0,b) coordinate should either be required or somehow banned, as the work with and without the y-intercept given is of considerably different difficulty.