Parabolas

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 Ax2 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