Precalculus: Exploring the Parabola

In problem 1, students will use a sheet of paper to explore parabolas. They will start by marking a point on the center of the paper and producing a series of folds along one of the longer edges that pass through this point.

Tracing along these straight-line folds should produce an envelope of lines, and the locus formed by the paper folding gives and approximation of a parabola. Students may use Cabri® Jr. to do a similar exploration.

Students move on to fitting a parabola, they use the formula 4p(y - k) = (x - h)² to assist them in their exploration.

At the end of this activity, students will be able to write and graph an equation of a parabola with vertex at (h, k) and axis of symmetry x = h or y = k. Students will also be able to derive the formula for any conic.