On the PA day I learned a new trick that Desmos can do.

First of all, you can insert images onto axes, which is cool.

The next thing you can do is to model things seen in the image. For instance, the water fountain creates a parabola. We can play with various expressions until we get one that’s close. Give it a try. Add an expression in factored form y=a(x-r)(x-s). Play with values for a r and s until you make the graph fit.

Another way to approach this task is by regression. You can insert a table of values, and fill the x and y columns with points that would be on the parabola in the picture. Be sure there are at least 3 points in your table.

To get the curve of best fit we use a tool called a regression. You need to be careful of the syntax. Type y1~a(x1-r)(x1-s) the 1s included tell desmos that you are dealing with table of values 1. The ~ tells desmos to make the curve of best fit. A curve will show on your screen, and a legend will appear beneath your expression in the sidebar showing the values for a, r and s.

The same thing works for a line of best fit.

You could just play with y=mx+b until the line you create models he slope of the ramp shown, or you could make a table of values and do a linear regression. Insert a table of values, include at least 2 points, and then insert the following expression Y1~mx1+b and desmos will create the best fit line and equation to match.

This is a powerful feature! Graphs with desmos allow you also to easily interpolate and extrapolate too. Touch or click anywhere on the lines/curves created to get the exact coordinates. Intuitive, eh?

Using the program through the website allows you to sign in with your google account or desmos account, and save your graph. The app wont let you save yet.

Give it a try tonight. See what you can do.