Parabolas

 History  Equation  Graph  Applications

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

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

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.

Identify the parabolas in the pictures

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