Constructing parabolas

A. In order to construct a parabola, we need to first start with a line AB. Next let point C be any point not on line AB.

Next we need to place some arbitrary point D on line AB and construct a perpendicular line through the construct point.

Now, construct a segment from point C to D, and then construct the midpoint E of the segment CD.

Finally, construct a perpendicular line through point E, and label the intersection with the line perpendicular to AB, F.

Below the parabola, there is an animation of the parabola being drawn.

Now that we have a construction of the parabola lets see how it is traced. In this situation, the trace point is F, and the point D is animated in order to form the red parabola.

Animation 1

B. Now we will consider another way to construct a parabola. This time lets select the line EF to trace instead of the point, and still allow point D to be animated. Here we see that the graph forms lines that are tangent to the vertex of the parabola instead of tracing the actual parabola.

Animation 2

Now through our exploration, we have discovered two different ways to construct a perfect parabola! Now, a new challenge is for you to explore new ways to construct similar parabolas.

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