You can fold many creases in a piece of paper that define a parabola.
Draw a dot on a piece of paper in "landscape" orientation half way across and about 5 cm (2 in.) up from the bottom edge. The dot can be anywhere on the paper, but this placement will yield a parabola that looks like the image above.
Fold Fold the bottom edge of the paper up so that it touches the point. Make a crease and open the paper again.
Fold repeatedly so that the bottom edge touches the point you drew at many different spots along the edge. Crease and open the paper each time you fold. The many creases will form a parabola.
The point you drew is the focus of the parabola and the bottom edge of the paper is the directrix.
Thomas Hull's book Project Origami: Activities for Exploring Mathematics offers an excellent activity that mathematic teachers can use to lead the advanced high school students through a proof of this method of folding a parabola.