# GeoGebra GeoGebra is free and multi-platform dynamic mathematics software for learning and teaching. It has received several educational software awards in Europe and the USA.

• #### Factorised Parabolas

This applet provides a visual understanding of the factorised form of a quadratic in the form
y = a(x - b)(x - c) where a is the shape, and (b,0) and (c,0) are the x intercepts. The equation of the graph, and the vertex can be hidden. Sliders are used for a,b and c. This applet was supplied by Priscilla Allan, Pakuranga College. Year / Level: Year 10+
• #### Patterns

The slider provides 10 different patterns made of graphs. The idea is to reproduce the pattern by entering the required equations into the input box. It can be used as a class exercise using the data projector, where students write down the equations, or if students have a computer they could work on it directly. This applet was supplied by Priscilla Allan, Pakuranga College. Year / Level: Year 10+
• #### Lots of Graphs

This applet shows linear, parabola, exponential, sine and cosine graphs. The big idea is that they all work on the same sliders and the connections between the transformations of different types of graphs are made easy to see. This applet was supplied by Priscilla Allan, Pakuranga College. Year / Level: Year 10+
• #### Exponential Curves

This applet shows the basic exponential function with some transformations using sliders.
The form a^(x - b) + c is used, and the line y = c is displayed as a feature of the graph. This applet was supplied by Priscilla Allan, Pakuranga College. Year / Level: Year 11+
• #### The Mid-Point Theorem

GeoGebra is ideal for any geometry application. The Level 2 Co-Ordinate Geometry Achievement Standard states that "appropriate technology" can be used. Therefore if your students have access to a computer and the software they could use it to solve any of the problems. This applet gives you a good illustration of the mid point theorem when given 2 points. With a few tweaks and changes you could easily add the distance formula as well.
• #### Linear Programming

A typical linear programming question goes along the lines of two products x and y are selling. The total units sold of both products is 14. Product x sells for twice the price of product y and when sold together reach a total of \$20. What is the maximum profit attainable. This GeoGebra applet illustrates the problem. By moving the profit point around the constraint lines you can see how the profit changes. Year / Level: Year 13
• #### Linear Programming (2)

This GeoGebra applet revolves around maximising the equation 3x + 4y given certain constraints. As with the Linear Programming applet it allows you to move the profit point around the area and then allows students to see where the maximum profit can be attained. Year / Level: Year 13
• #### Limits

Differentiating from first principles, showing the limit as h tends towards zero. This applet is just like the pictures in the text and workbooks, except it actually moves. Point P and Q are points on a funtion curve, with a line through them. You can select to show the three gradients, and see the limit in action. If point P and Q are on top of each other the gradient of the line PQ is undefined, but the gradient of the tangent at P, and the tangent at Q are the same. It is fantastic to be able to show exactly what is happening rather than just using a static diagram. This applet was supplied by Priscilla Allan, Pakuranga College. Year / Level: Year 13
• #### Integration

This applet is included to let people know just what Geogebra can do. The applet graphs the area under a graph and shows integration in action. This applet was supplied by Priscilla Allan, Pakuranga College. Year / Level: Year 12+
• #### Numerical Integration

This applet illustrates numerical integration using rectangles and trapeziums. This applet was supplied by Priscilla Allan, Pakuranga College. Year / Level: Year 13