How to find the foci, center and vertices, and asymptotes of a hyperbola

The video tutorial covers the process of transforming an equation into its standard form, plotting asymptotes, and sketching the graph. It begins with combining and rearranging terms, followed by completing the square. The tutorial then simplifies the equation, identifies the center and vertices, and calculates the foci. Finally, it determines the asymptotes, providing a comprehensive guide to graphing hyperbolas.

What is the first step in determining the orientation of a parabola?

Explain the process of completing the square for the equation provided.

Explain the importance of the standard form of a hyperbola.

What is the significance of the center in the context of hyperbolas?

What does it mean for a hyperbola to have a vertical transverse axis?

How do you determine the vertices of a hyperbola?

How do you find the foci of a hyperbola?

Describe the relationship between a, b, and c in the context of hyperbolas.

What is the formula for finding the asymptotes of a hyperbola?

What steps are involved in graphing a hyperbola?