Porabolas off the Origin

[Guest]

Hey. I'm stuck on a particular part of my homework which I do not know how to figure out at all. So I was wondering if someone could help.

I'm supposed to find the vertex, focus, directrix, and axis of symmetry.
I understand how to find everything except the focus. I know there's a formula for finding it but my teacher did not teach me that, insted taught a different method which I'm not sure I quite know what she did, or understand it.

For example:

y=(x+2)^2+3

V(-2,3)
F(-2 ?)
Directrix: ? (I have to know the focus for this)
Axis: x=2

So can anyone help me find the vertex without using the formula?

 

[Gene]

Write it in the form
(x - h)2 = 4p(y - k)
Which is almost what you have
y=(x+2)^2+3
(x+2)^2=1*(y-3)
You know x=h & y=k gives the vertex
4p=1
p=1/4
The directrix and focus are p above and below the vertex.