## Parabola

## by

## Becky Mohl

### 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.

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### 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.

###

### 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.

### 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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