The document discusses parabolas and provides their vertex, standard, and equation forms. It gives an example of graphing the parabola y^2 - 6y - 8x + 49 = 0, finding its vertex at (5,3), focus at (7,3), and directrix of x = 3 since it opens to the right with p = 2.

1. January 05, 2012
The Parabola The set of all points equidistant from
a fixed point (focus) and a fixed line (directrix)
The vertex form of a parabola is given by:
y = (x-h)2+k, where (h,k) is the vertex.
The standard form of a parabola is
1. (x-h)2=4p(y-k) where (h,k) is the
vertex
OR
2. (y-k)2=4p(x-h) where (h,k) is the
vertex.
Equation 1, the parabola opens up or down
Equation 2, the parabola opens left or
right
focus
vertex
directrix
p is the distance from the vertex to the
focus and the distance from the vertex to
the directrix

2. January 05, 2012
Example: Graph the following parabola and
list the vertex, focus and directrix
y2- 6y -8x + 49 = 0
1) This parabola opens left or right
2
because of the y .
2) We need to get y's on one side and
x's on the other side
2
y - 6y = 8x - 49
3) Now complete the square on the y's
2
y - 6y + 9 = 8x - 49 + 9
2
(y-3) = 8x - 40
4) The coefficient in front of the x and y
must be a 1 (according to our formula).
2
(y - 3) = 8(x - 5)
2
(y - k) = 4p(x-h) original formula
so…4p = 8
or…p = 2
Our parabola has a vertex at (5, 3) with a p
value of 2. It opens right because the p is
positive.
Focus: (7, 3)
Directrix: x = 3