1. Parabolas  History  Equation  Graph  Applications

2. History  Studied by Menaechmus, pupil of Plato  Was written about by Euclid  Named by Apollonius  Focus and directrix considered by Pappus  Galileo showed projectiles follow parabolic paths

3. Equation  The set of points in a plane that are equidistant from a point (focus) and a line (directrix).  Standard Form  y = Ax 2 + Bx +C  y = a(x - h) 2 + k

4. Graph  What are some examples of a parabola? Where do we find them in the world?  Try graphing a parabola.  Click on picture of the parabola.  Go to file New Sketch.  Make a random point.  Make a random line.  Select both the line and the point.  Press Play and watch the parabola form.

5. Identify the parabolas in the pictures

6. Applications  To map the path of projectiles, like a baseball, in a homerun, a golf shot, or a cannonball.  Show the path of light rays  Ideal shape for cables on a suspension bridge  Shape of a water spout