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Intersecting Tangents of a Parabola

Construct two tangents to a parabola and investigate the coordinates of their point of intersection.

Barrie Galpin

Fach:

Schlagwörter Quadratic, Simultaneous equations, Reasoning, Coordinate Geometry

A detailed 4-page Handout guides students, step by step, through the necessary construction starting with a new, blank TI-Nspire document. They are then able to move the points on the parabola and see the resulting coordinates of the point of intersection.

After collecting a range of numeric data they are encouraged to predict a general algebraic statement for the coordinates of the point of intersection. Next they are guided towards an algebraic proof of the result. Finally several extensions to the investigation are suggested.

As well as Teacher Notes, there is also a Marking Grid, which will be helpful in assessing students? completed work.