Expert: Richard J. Raridon - 3/15/2004

Question
Can you tell me please how to graph a parabola from its equation  I also need to label the vertex, focus, and directix.  Then, I need to write the standard equation of the parabola.  thanks.

Answer
The standard equation for a parabola facing left or right is
(y-k)^2 = 4a(x-h)
For one facing up or down you have (x-h)^2 = 4a(y-k)
You can graph it by putting in x values and calculating y values or vice versa.  
The vertex is at (h,k)
the distance from the vertex to the focus is a and the distance from the vertex to the directrix is a.
For example, if you had (y-2)^2 = 8(x-3),
the vertex would be at (2,3)
the focus would be at (4,3)and the directrix would be at
(0,3)