How to find the focus and directrix when your vertex is at origin

The video tutorial explains how to analyze a parabola given the equation X^2 + 6Y = 0. It covers determining the orientation of the parabola, finding the vertex, focus, and directrix, and calculating the value of P. The tutorial also includes a sketch of the parabola, emphasizing the importance of understanding the value of P in relation to the vertex and focus.

How do you calculate the value of P in the context of a parabola?

What is the relationship between the focus and the directrix of a parabola?

Describe the process of sketching a parabola given its vertex, focus, and directrix.