Creating an algebraic activity with Geogebra.

We will work on creating an activity along the lines of the one at http://www.slu.edu/classes/maymk/GeoGebra/QuadEqn.html. We want to look at a generic quadratic polynomial. We start with a clean GeoGebra window and type f(x) = a x^2 + bx + c in the input bar.

Since we have not defined the parameters a, b, and c, we are asked if we want to make them sliders.

We say yes and sliders are created for us.

By default, sliders run from -5 to 5 and are horizontal. We would like to make them go from -10 to 10 and be vertical. If we control click on a slider we get a menu fro making changes. We want to select “Object Properties”.

We want to use the preferences window that shows up to change the range to [-10, 10] and the orientation to vertical. We can do this one slider at a time, or use shift-click to work on several at a time. We also uncheck the box to fix the object because we want to rearrange them.

We now have an applet for visualizing the graph of f(x)=a*x^2+b*x+c. with the parameters moved to different values. We also close the algebra window to give more room in the graph.

Depending on your operating system, you can either right-click or control-click on a slider to start animation of the slider.

Once animation is started there is a run/pause button in the lower right corner to control if the animation is on or off. Recall that control-click brings up a menu with object properties and selecting properties gives a preference window. That window lets us control the speed of the animation.

The real lesson of this handout is adding text to make the tool more useful to the students. We want to have a text that includes a preset formula and also includes the value of the quadratic equation with the parameters filled in. We chose the text tool and click on the graphics window where we want text.

First we type the text we want. Notice that you are given a preview of how it will appear. However we also want the value of f so we select f from the menu of objects.

The result in the preview combines text with live values that we change as we move the sliders.

If we select the LaTeX option our text will be nicely typeset. (More on LaTeX in a later activity.

We similarly produce texts to give the roots of the equation and then the equation in factored form.

Note that the box for object can be edited to give more complicated expressions.

The equation is simpler if we first define Root1=(-b+sqrt(b^2-4*a*c))/(2*a) and

Root2=(-b-sqrt(b^2-4*a*c))/(2*a)

© Mike May, S.J., 2016