This activity involves exploring some of the properties of a paraboloid. It will include concepts from Algebra 2 (Conic Sections), Geometry (Parallel Lines, Perpendicular Lines, Reflections, and Proof), and Calculus (Derivatives, and Tangent Line).
Before the Activity
Creating the TI-Nspire graph will take approximately 45 minutes. Proving that all rays parallel to the y-axis will be reflected to the focus is left to the student as homework and may take a few days.
During the Activity
Follow the directions in the Word or pdf file. A completed graph is included as a .tns file.
After the Activity
Students may need several days to complete the proof on their own. They may also need "hints" along the way.