Write the equation in standard form by completing the square to find vertex, focus and directrix

The video tutorial explains how to complete the square to convert equations into conic section form. It begins with an introduction to the concept, followed by setting up the equation by arranging terms. The process of completing the square is detailed, including finding the value that completes the square. Finally, the tutorial demonstrates how to identify the vertex, focus, and directrix from the completed equation, providing a comprehensive understanding of the topic.

What steps must be taken to ensure the equation remains balanced when completing the square?

Describe how to sketch the graph of a conic section based on the vertex and the value of P.