Graph the following parabola (x-2)^2=(y+1) list the vertex focus and directrix

Rearranging, we have:



That means we have the form

where h and k are the vertex coordinates.

The directrix is the same distance from the vertex as the focus is from the vertex.

Pardon my typo in my first post. That should be

Note, if we expand we get

The x coordinate of the vertex can also be easily obtained by using

Then, sub that value back into the quadratic to find its corresponding y coordinate.

Note, you have the form . This is a concave up parabola.

The distance from the vertex to the focus is .

Consequently, that distance is the same from the vertex to the directrix. You have found the vertex, so use that and find the directrix.

It will just be a horizontal line with coordinates y=some number. Look at the graph. That'll help.