The Parabola as the Locus of the Product of two Lines: Building Functions from Functions

Abstract

This paper presents another approach to vertical parabolas--namely as the product of two lines.  The locus in Geogebra (Hohenwarter, 2002) permits to produce this product and dynamically investigate changes in the parabola and relate them to its linear factors. This approach can be easily generalized to more linear factors, and to horizontal parabolas.  This approach relates to the Function Domain -- Building Functions in the CCSS.