Parabolas

What is a parabola?

• A parabola is the path a ball follows when it is thrown.
• A parabola is a curvy bowl shape:
  x	y
  -3	9
  -2	4
  -1	1
  0	0
  1	1
  2	4
  3	9

• A parabola is a polynomial of degree 2. It can be written in an expanded form like $f(x) = Ax^2 + Bx + C$ or a factored form like $f(x) = A(x - B)(x - C)$
• All the points on a parabola are the same distance from a special point called the focus as they are from a special line called the directrix.
• A parabola is the shape you get when you slice through a cone like this: