This activity was created so that students could explore the relationship between the parameter "a" and the distance between the focus and the vertex, and the vertex and the directrix, on their own without explicitly being told a formula for it. We know that research shows that if students can develop relationships between values on their own they will be more likely to remember that relationship longer, and understand the relationship more deeply, than they would if the teacher simply told them the relationship.
Hence, the GeoGebra applet was created to allow students to manipulate the different parameters of a quadratic function in vertex form and see how these parameters affected the distances between the focus and the vertex and the vertex and the directrix. The applet is meant to allow students to dynamically change the geometric ideas being presented so that they can draw their own conjectures about what is happening to the graph of the parabola.
The worksheet is meant to guide students through discovering this relationship. It should give the students a direction to go in without explicitly giving the relationship to them.
Hence, the GeoGebra applet was created to allow students to manipulate the different parameters of a quadratic function in vertex form and see how these parameters affected the distances between the focus and the vertex and the vertex and the directrix. The applet is meant to allow students to dynamically change the geometric ideas being presented so that they can draw their own conjectures about what is happening to the graph of the parabola.
The worksheet is meant to guide students through discovering this relationship. It should give the students a direction to go in without explicitly giving the relationship to them.