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Exploring
Geometric Constructions of Parabolas


 
This
activity is an introduction to geometric constructions of parabolas. We
will investigate their properties and characteristics. This activity has
been adapted from the following article: Olmstead, E.A. (1998). Exploring
the locus definition of the conic sections. Mathematics Teacher,
91(5), 428434.
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:
In this activity, students will use problemsolving 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. 

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