Writing the equation of a parabola given focus and directrix

The video tutorial emphasizes the importance of plotting in solving math problems, particularly focusing on the relationship between the focus, directrix, and vertex of a parabola. It explains how to graph parabolas, determine their orientation, and use the vertex form to simplify equations. The tutorial concludes by highlighting the significance of understanding these concepts to avoid common mistakes.

What does it mean for a parabola to open towards its focus, and how can you identify the direction it opens?

Describe the formula used for a parabola that opens horizontally and how the vertex coordinates are incorporated into it.