A few weeks back I found a file called randomlinegenerator.ggb in a shared Dropbox folder. A modified version of this file is embedded below.

Each time we press the "New Line" button, a new line is randomly generated in the form of ax+by=cb, with each of the parameters being a randomly generated integer between -10 and 10. Amazing, right? This my favorite Geogebra find of the month.

It turns out that the members of this team (Algebra) have used this tool in a variety of ways. One teacher had students practicing finding y-intercept and slope, another was having students find the equation of the line, and a third suggested use was for students to find solutions of the line. I had a lot of fun playing around with how to change the file to use for other types of functions. In doing so I learned some new commands along the way worth sharing (see below). I also added a checkbox so that the equation of the function can be revealed or hidden, similar to flashcards.

I've made a few of these files for other function types so far, but I'm waiting for some feedback before uploading more. I'll link to other flashcard files and ask questions at the bottom of this post. For now, you can view parabolas in vertex form from Geogebratube. You can also download this file and make modifications for other function types, or build your own file by following the steps below. Type each command into the input bar at the bottom of the screen and press enter.

1. a=RandomElement[{-1,1}]

This command chooses either -1 or 1 to be the a value. You can change the set of numbers in the list, but I wanted -1 and 1 to start with so students can focus on vertex, max/min, and horizontal and vertical shifts.

2. h=RandomBetween[-5,5]

This command randomly chooses an integer between -5 and 5, inclusive of endpoints.

3. k=RandomBetween[-5,5]

This command randomly chooses an integer between -5 and 5, inclusive of endpoints. I chose -5 to 5 for my h and k ranges so that it will be easy to see the vertex on the standard viewing window. This still gives me 121 possible vertices, each of which can be a maximum or a minimum.

4. f(x)=a(x-h)^2+k

This command creates a function called f, with the parameters of a, h, and k described above.

5. To add the button, select the button tool from the dropdown menu under sliders.

Then type UpdateConstruction[] into the Geogebra Script box. Type the name that you want for your button into the Caption box.

At this point you will have a random parabola generator!

To make this self checking like flashcards, there are two more steps. Next add a textbox that will display the function equation, then add a checkbox that will hide or show the textbox. I can add a post with directions for how to do this if there is interest. I feared that this post was getting too long so decided to stop here with Geogebra instructions.

Some questions that I have are:

- Should students be able to type a function into the input bar at the bottom of the page in order to check their guess? If so, students would reload the page when finished to get a new graph and delete the graph that was typed in by the student. I added this feature on the random absolute value graphs file below.
- For non-linear functions I chose the a parameter value to be either 1 or -1. Is this too limiting, or will this cause confusion later when students have a-values that are not 1 or -1?
- Anything else that would make Geogebra flashcards better? Are there other files on Geogebratube that are like flashcards?

__More random function generators:__
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