Creating the Dynamic Figure

We will now show you how to create the worksheet Shape of a Slope Function step by step. First, you need to construct the dynamic figure including the quadratic polynomial f, point P and the tangent line t as well as a special point M whose y-coordinate equals the slope of the tangent line t. To do this, you can use the interactive applet below that represents the user interface of GeoGebra but includes a customized tool bar to simplify the construction. It enables you to do the construction and export it as a web page. Since this setting should only provide an environment to gain first experiences with the use of GeoGebra while reading this article, we recommend to install GeoGebra and to have a look at the GeoGebra Quickstart document for additional information.

General Hints for the Use of GeoGebra

• In order to activate a tool you need to click on the corresponding toolbar icon.
  Tip: Note the toolbar help next to the toolbar icons in order to find out how to use the selected tool.
• If you type an algebraic expression into the input field at the bottom of the GeoGebra window you need to hit the Enter-key in order to process this information.
• Right click (Mac OS: ctrl-click) an object in order to
  • Show / hide the object
  • Rename the object
  • Delete the object
  • Change properties of the object
• A slider is the graphical representation of a number. If you create a number using the input field you need to show the number in order to get the corresponding slider.

Step-by-step Instructions

1. Create the parameters a = -0.5, b = 2, and c = 4 using the input field or the "Slider" tool.
2. Define function f(x) = a x^2 + b x + c using the input field.
3. Activate the tool "New point". Move the mouse over the graph of function f and click on it when it is highlighted to get a point on the graph. Rename this point to P. Tip: Check if point P really lies on the graph of function f by selecting the tool "Move" and dragging point P along the graph.

4. Select the tool "Tangents" and successively click on point P and the graph of function f. Rename the tangent to t.
5. Use the command m = Slope[t] in order to get the slope triangle of the tangent line.
6. Create point M by typing M = (x(P), m) into the input line. Tip: x(P) gives you the x-coordinate of point P.
7. Export your dynamic figure as a dynamic worksheet by selecting "File" - "Export" - "Dynamic Worksheet as Web page (html)..." in the menu bar.