Saturday, November 28, 2015

Using Desmos to find the quadratic model of a real-world image

Desmos is at it again...
Since I started using Desmos more regularly this summer, I have found that it is gradually replacing a number of my other math software options.  The latest instance happened when my algebra 2 students were finding examples of things that take the form of a parabola.

In the past, I have had students find an example of a parabola in their everyday lives and snap a picture of it.  I've seen images of everything from the McDonald's logo to a water fountain to a mug shot of someone's jaw line.  Then I would have students upload their images into Geometer's Sketchpad and construct a number of points along the parabola.  Here is an example...

After that, I would have the students enter the ordered pairs into a TI-84+ or TI-Nspire graphing calculator, find the regression equation, and go back to Sketchpad and graph the function on top of the image.  Again, an example:

Some years I would have students explore around with vertex form a bit to try to fit a quadratic model before we found the regression equation.  But it was a painfully long process to bounce back and forth between Sketchpad and graphing calculator.

This year, I decided to direct students to Desmos to compute the regression equation.  After all, we had used Desmos to find linear regression equations earlier in the year and all students had access to Desmos w/ our 1:1 laptops.  (Not all students would have a TI-84 or Nspire to use in years past.)

It turns out the students had a great idea. Why use Sketchpad to plot the points and graph the regression function?  Why not just use Desmos?  I loved the idea and it really simplified the process.

Students simply inserted their images into Desmos, plotted points on the parabola, created a table with their ordered pairs, and found the quadratic regression equation (& graph) all in one place.

Follow this link for an example (image shown below).

Better yet, using the sliders in Desmos is a breeze.  Simply insert an image of anything parabolic and have students fit the model using vertex form.

1 comment:

  1. Mark-This is a really slick lesson! I have had students do similar things in the past, but not using Desmos. I really like how your graphs have turned out.
    The one thing I had my kiddos do was create a poster explaining their process (especially if they found the vertex form of the parabola). They had to walk through their steps of not only creating the visuals and the graph, but also the math. We then printed them, laminated, and hung them out in the halls of the school. The kids got some great comments on the real-world math.