Algebra + Desmos: The Power of Zoom to Explore Graphs

This is a simple exploration for students to use Desmos on iPad to “look around” the Cartesian plane using Pinch to Zoom in and out. The students manipulate the graph to set the axes so the key points are visible.

The Why

Do your students say, "I can't see the graph? It's not there!" when they graph a function using the wrong axes settings? The graph IS there, it's just not on the screen.

I love giving students the opportunity to explore graphs using Pinch to Zoom. The abstract idea that the Cartesian plane extends infinitely in both (x and y) directions can be challenging to understand and this exploration is a safe way for students to “look around the graph” and see what happens when they zoom in and out.

The Benefit

This exploration will pay off when students are tasked with creating their own graphs by hand and need to decide how to set up the numbering system of each axis.

The Launch

The screenshot below is from the Desmos app on iPad. The function f(x)=x^2+5x+6 is graphed, but is not visible. This is where you should launch the exploration for your students. Ask questions such as, “Why can’t you see the graph?” And, “If you know it should be there, what can you do to find it?”

The screenshot below is the result of tapping and pulling the y-axis down far enough to show the graph on the screen.

The key points of the graph are still not clear, though. From this view (above) it is too difficult to determine the minimum, zeros, and y-intercept.

The How To

This is the best part of this exploration! Did you know you can zoom in or out on an individual axis without impacting the other? You can! Here, I want to zoom in on the x-axis only. I prefer to use both hands to do this so I can carefully manipulate the graph. The video below shows how to do this.

The power of zoom allows students to explore graphs in a way that cannot be done without iPad. I encourage you to try this with your students and let them explore more!