This document provides an overview of parabolas including their key properties and examples of how to graph and write equations of parabolas. It defines that every point on a parabola is equidistant from the focus and directrix, with the directrix perpendicular to the line of symmetry and the vertex halfway between them. Examples are given of finding the focus, directrix, and graphing parabolas given these features as well as writing the equation of a parabola given its directrix.

1. 6-5 Parabolas
Objectives:
1. Graph parabolas.
2. Write equations of parabolas.

2. Properties of Parabolas
 Every point on a parabola is
equidistant from a point called the
focus and a line called the
directrix.
 The directrix is
perpendicular to the line
of symmetry.
 The vertex is halfway
between the focus and
directrix.

3. Parabolas can open vertically or
horizontally.
Equations only good for vertex at (0, 0).

4. Example 1:
Find the focus and directrix of
each parabola and tell which
direction it opens.



5. Example 2:
Write an equation of the parabola
with vertex (0, 0) and directrix
x = 2 and sketch its graph.

6. You Try!
Write an equation of the
parabola with focus (0, 3) and
directrix y = -3. Sketch its graph.

7. Example 3:
Find the vertex, focus, and
directrix, then sketch the graph.
y = 2x2 – 8x + 3