How to find focus, directrix, and direction of opening?

Here is one you tube, I have not watched it but it will probably help.

There are many others if you don't like this one :)

 

https://www.youtube.com/watch?v=1Lwi8cOdqCU

 

Parabola

 

\(\boxed{(x-h)^2=4a(y-k)}\)

 

Vertex   is  (h,k)

 

a not equal 0

concave up if a>0    positive

concave down if a<0   negative

 

The focal length is |a|

 

The focal point will be (h,k+a)

 

The length of the latus rerctum is 4a    The equation of it will be y= k+a

so

The points at the end of the latus r****m will be  (h-2a,k+a)  and (h+2a,k+a)

 

What else do you want to know?

 

Here is an excellent graphing calc so you can play around with some different equations and see what happens.

 

https://www.desmos.com/calculator