Mathematics: The students will develop geometric constructions of parabolas as loci of lines, and as loci of points. They will use the distance formula to algebraically derive the standard form of a quadratic function. Students will conjecture and prove the following theorem:

• The distance from the parabola to its focus and the distance from the parabola to its directrix are equal.

In this activity, students will use problem-solving skills to simulate the geometric construction of a parabola using The Geometer’s Sketchpad. Students will also be asked to conjecture and prove the aforementioned theorem.

Technology: This activity uses several Sketchpad commands such as: Line, Segment, Midpoint, Perpendicular Line, and Locus.

The following sketch illustrates a geometric construction of a parabola using The Geometer’s Sketchpad.