Is It a Parabola?
A parabola is a special kind of curve. Each point on the parabola is as far from a certain line (called called the directrix) , as it is from a certain point called the focus. In this worksheet, you'll get to decide whether the curve followed by a stream of water in a fountain is a parabola. You may show or hide the photo of the fountain at any time. First, to learn how the shape of a parabola changes when the focus and directrix change, you'll move the red pòints and the red line. Don't be shy! Have fun with it, and move them wherever you like. Then, for practice, you'll try to make the red parabola fit a black 'target' parabola. You'll have to click on one of the little check boxes to show or hide the black parabola. If you need more help, you can click on another little box to show or hide the black parabola's focus and directrix. When you feel that you've practiced enough, you'll click on a check box to show the stream of water. (Hide the black parabola, of course!) Then, you'll move the red directrix and focus to try to make the red parabola fit the curve followed by the stream of water. Take your time, and do the best you. Can you make the red parabola fit the stream? If so, then the stream is a parabola, with the same focus and dirctrix as the red parabola.
Discuss your results and your decision with your classmates. Do they agree with you?