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.

1. March 31, 2008 am31 4:10 am 4:10 am

My parabola would be a flatline (like you don’t want to see on the heart monitor) since it’s (0,8) (0,8) (7,8)

2. March 31, 2008 am31 5:24 am 5:24 am

$y=ax^2 +bx + c$, but for you, you have all sorts of choices:

y = kx(x-8) , choose whatever k you like. If you were August 18, a and b would need to be 0 – I’d call that a double-degenerate parabola (just to entertain the kiddies).

And (7,8)? Way to make me feel old, dude!

March 31, 2008 am31 6:23 am 6:23 am

so had exactly your idea at first, but i wanted to do something cool with the idea, but was thwarted and stymied (temporarily… i hope)

http://samjshah.wordpress.com/2008/03/31/birthday-polynomials/

sam.