Tag Archives: parameter

Quadratic Explorations

The standard form of a quadratic is $y=ax^2+bx+c$.  Most students understand the effects of a and c on the graph of the parabola, but what does b do?  I hinted at this problem earlier, but just created and uploaded a GeoGebraTube Web document to model the problem.

In class, that’s about all I give before releasing my students to explore on their own.  As always, my students are required to do two things:  state their conjecture and prove that it works.

Results from my students coming in a future post.

Quadratic Explorations

I first encountered this problem about a decade ago when I attended one of the first USACAS conferences sponsored by MEECAS in the Chicago area.  I’ve gotten lots of mileage from it with my own students and in professional circles.

For a standard form quadratic, $y=a*x^2+b*x+c$, you probably know how the values of a and c change the graph of the parabola, but what does b do?  Be specific and prove your claim.