# Day 87: Curve-fitting with Desmos

*College-Prep Physics*: Curve-fitting by hand can be tedious and linerization can be confusing. But curve-fitting with technology has its drawbacks, too — Excel is too unweildy and Logger Pro’s buffet of functions quickly has students blindly finding the function with the lowest R value.

Enter Desmos: While it doesn’t produce pretty labeled graphs like Logger Pro, I LOVE the slider function for curve fitting. (I know Logger Pro can do this, too, but it’s so much simpler in Desmos.) So today, everyone graphed their paragraph data from several weeks ago in Desmos. Then we reviewed the 4 types of functions we’ll be encountering this year and their characteristics:

Then we looked at several data points to see what doubling *x* (paragraph width) did to *y* (paragraph height). Did height double (linear), quadruple (quadratic), halve (inverse), or quarter (inverse square)? Now that we knew it would be an inverse relationship, we added to Desmos a “*k=*1″ line and a “*y* = *k*/*x*” line. Then we dragged the slider for *k* until we get a good fit for the data.

So in the example in the first picture, we get *y = *6.8/*x*. But what does *y *represent? What does *x* represent? What are the units for 6.8? While Logger Pro automatically figures that out, I like that Desmos forces kids to wrestle with those questions. After some analysis, we see the relationship in the first picture to be *height* = (6.8 cm^{2})/*width*.

Now that we walked through that example as a class, we did a follow-up activity which looks at the effect of font size on the height of the paragraph, which I modified from here: http://bestcase.files.wordpress.com/2012/08/paragraphshandouts.pdf

To mix things up, I had each group member analyze a different font. My handout is here: LAB measuring paragraphs FONT SIZE 2014 Low Tech

Once the graphs are done, students get a unique URL for their graph that they can share with me, or download an image of the graph for inserting into Word documents or printing and pasting into lab notebooks.

PS: Sorry for being MIA the previous 9 days. College-prep students were working on their midterm projects for the first 4 days, and the remaining 5 days were midterm exam days where students took buffet quizzes and handed in their projects.