Good ideas for quadratic problems?

Question

I'm a high school math teacher and am trying to come up with a good word problem that will have students write (but not solve) a quadratic function. Thus far, I've had them calculate trajectories (in November I used "Punkin' Chunkin" as a way to introduce quadratics) and I've also come up with some area problems, but I'm running out of ideas for word problems that would require them to write a quadratic function.

I want to avoid writing one that is of the type where sales go down as price goes up because I've always found that model to be a little too artificial.

Anybody else have any good ideas for me?

I want to avoid writing one that is of the type where sales go down as price goes up because I've always found that model to be a little too artificial.

Anybody else have any good ideas for me?

Jeremy · Accepted Answer

i was also a secondary school mathematics teacher...

there was a 'writing' strategy which I had acquired in my master's program:

the student imagines that they are a quadratic equation (or linear equation, or a system of equations etc).

they are to write a biography of themselves. 
to ensure the students are properly aligned with what you what them to be thinking abuot, you would include a rubric.

for example, in the rubric you could ask:

what are you family members when a > 0?
a < 0?
what happens when a = 0?

which includes their family (of curves).

if they're well-rehearsed with the graphs of quadratics you could also include when there is 0, 1, or 2
x-intercept(s) and expand on that with the discriminant. or even expand on the discriminant with completing the square of yourself (the student as the quadratic).

actually, you could write an autobiography of the discriminant of a quadratic alone lol.

don't forget to include all gardner's levels of intelligences, hit all levels of bloom's taxonomy, and ensure you reach the ELL students as well as all the students with learning disabilities that have an IEP in the mainstream classroom.  have fun :)

I still haven't met another high school math teacher who actually know's who the father of modern mathematics is: Everiste Galois.  it's a shame i wasted my prestigious degree in mathematics by going into public education.

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Good ideas for quadratic problems?

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