**Valerie Russell**

**Assignment 6** - **What is a Parabola?**

A parabola is a locus of points equidisatant from a line, called a the directrix, and a fixed point called the focus.

.Foci Point

**___________________________** Directrix

A parabola is really a symmetrical curve. There is a straight line, called the axis

of symmetry, which passes through one point of a parabola, the vertex, and

separates it into two parts that are mirror images of each other. The fixed point

(focus) in the diagram is labeled A. The directrix is the horizontal line

below the vertex. The vertex is the maximum or minimum point of the

parabola.

__Constructing a parabola using GSP:__

In order to construct a parabola you must first construct a point (called the focus - A) and a horizontal line (called the directrix - B). Pick any point on the horizontal line and draw a perpendicular line through the point. Construct a segment from the foci point to the point on the horzontal line and find the midpoint of that segment. Construct a perpendicular line through the midpoint. Use the display feature on GSP to animate the point of intersection of the two perpendiculars constructed and watch the formation of the parabola.

To see an animation of how a parabola is formed from the focus and the directrix, please click on See Animation.

__Construction of the Parabola using Paper Folding__

One way to model a parabola is to draw a line and a point near the line on a sheet of patty or wax paper. Find the points that appear to be equidistant from the point and the line and connect them folding the paper. Do this many times. The resulting curve is a parabola. Here is a list of easy instructions you can use with students if you do not have access to a computer.

**Students can make several conjectures using this hands on activity.**

__Another Construction of the Parabola__

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