Ok, I've been given this:
and I have to find the vertex, focus, and directrix of this graph.
I know how to find the vertex. In this case, it is at the origin. However, I don't have the slightest idea how to find the focus or the directrix.
Help would be appreciated here
The focus should be "inside" the parabola. Since we have a parabola that opens to the right, the focus should be to the right of the vertex. And its distance from the vertex is , with .
The directrix should never touch the parabola and a perpendicular drawn to the directrix from the vertex will have length , which is why we must have the line .
Edit: Your book has the wrong focus.