GeoGebra Essentials 8 – Graphs and their Properties

This is the eighth tutorial in the GeoGebra Essentials Series. If you are not familiar with GeoGebra, you may want to read the Introduction to GeoGebra post and earlier tutorials.

In the tutorial below, menu commands, located in the menu bar, are in brown bold text, and submenus are denoted by the > symbol. For example, Options>Labeling>New Points Only means, click the Options menu, choose Labeling from the list, then select New Points Only. The tool texts are colored orange. For example, New Point means the new point tool. Text that are to be typed in the input box are colored blue.

In this tutorial, we learn how to graph functions using GeoGebra. First, we  graph a function, then determine its critical points (minimum, maximum, inflection point, roots) using GeoGebra keyboard commands.  Then we get the derivative of the function. We also construct a point on the function and a line tangent through that point. We explore the characteristics of the tangent line in relation to the graph of the function and its derivative.  The final output of our tutorial is shown above.  » Read more

GeoGebra Essentials 7 – Using the Keyboard Commands

In the previous tutorials in the GeoGebra Essentials Series, we have discussed how to construct mathematical objects such as points, lines, line segments, circles and other mathematical objects using the mouse and the tools in the Toolbar.  In this post, we  learn how to construct these objects using keyboard commands. In particular, we are going to create an equilateral triangle.

Step by Step Instructions

In this post, we create equilateral triangle ABC. The construction is very similar to GeoGebra Tutorial 2 – Constructing an Equilateral Triangle.

1.) Open GeoGebra. Select Algebra & Graphics in the Perspective panel to open the Algebra & Graphics window

2.) To plot point A with coordinates (1,1), type A = (1,1) in the Input Bar and then press the ENTER key on your keyboard. Now plot B = (5,1).

3.) To construct segment AB, type segment[A,B].

4.) To construct a circle with center A and passing through B, type circle[A,B]. Now, construct a circle with center B passing through A.

5.) Now, to intersect the two circles, type intersect[c,d]. The names c and d are the name given by GeoGebra to the two circles (see Algebra view). Names, usually small or capital letters, are given to each object in GeoGebra. Do not confuse the names with equations.

6.) Next, to polygon ABC, type polygon[A, B, C].

The Final Output

7.) Now, hide the circles and point D by right clicking them and clicking Show Object and we are done.  As we can see, we cannot do everything using keyboard commands. 

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