I can find the vertex, focus and directrix but I can't find the rest of the points on the graph!
I can find the vertex, focus and directrix but I can't find the rest of the points on the graph!
There is one other important part of the parabola and it is called the latus rectum ...
It is the line the passes the the focus and ends at two points on the parabola. It lets you know how wide the parabola is supposed to be
Once you have drawn the Vertex and Latuc Rectum, you can connect the dots.
The length of the latus rectum equals 4a
NOTE:
if a > 0 and the equation begins y = , then the parabola opens upward
if a < 0 and the equation begins y = , then the parabola opens downward
if a > 0 and the equation begins x = , then the parabola opens to the right
if a < 0 and the equation begins x = , then the parabola opens to the left
EXAMPLE:
If your equation is y = 1/8 (x - 1)^{2} + 1
Vertex (1,1)
Focus (1,3)
Directrix y = -1
Latus Rectum = 1/a = 8
Therefore, the graphing points that you would trace are V (1,1) (-3,3) and (5,3).
Comments
Which other points are you looking for? x-intercepts and y-intercepts?