Step by step graph and identify the foci, center, and vertices of hyperbola

The video tutorial covers the identification and plotting of hyperbolas. It begins with recognizing the components of a hyperbola, such as a^2, b^2, and c^2, and proceeds to calculate and simplify these values. The tutorial then explains how to plot the hyperbola using the center and axes, determine the positions of vertices and foci, and label them correctly. It also covers deriving asymptote equations and graphing techniques using the box method. The session concludes with a practice problem for students to apply their learning.

What is the relationship between a^2, b^2, and c^2 in a hyperbola?

• a^2 - b^2 = c^2

• c^2 = a^2 - b^2

• c^2 = a^2 + b^2

• a^2 + b^2 = c^2

How do you determine the center of a hyperbola?

• By calculating the distance between the vertices

• By using the coordinates of the foci

• By finding the midpoint of the vertices

• By identifying the values of H and K

What is the distance from the center to the vertices in this example?

• 2 units

• 4 units

• 2√5 units

• 5 units

How should you express the vertices when dealing with radicals?

• Convert to decimals

• Leave in radical form

• Simplify to whole numbers

• Express as fractions

What is the formula for the asymptotes of a hyperbola?

• Y = ± a/b * X + H - K

• Y = ± a/b * X - H + K

• Y = ± b/a * X - H + K

• Y = ± b/a * X + H - K

What method is suggested for graphing the asymptotes?

• Box method

• Slope-intercept method

• Intercept method

• Point-slope method

What is the purpose of creating a box with the co-vertices?

• To calculate the distance

• To determine the slope

• To find the center

• To graph the asymptotes