Hyperbola Graphs and Equations

The video tutorial explains how to match hyperbolic equations to their corresponding graphs by analyzing the standard form of the equations and identifying the characteristics of the hyperbolas, such as the orientation of the transverse axis and the center point. The tutorial walks through the process of converting equations to standard form, determining the center, and matching each equation to the correct graph. It concludes with a verification of the matches.

What determines the orientation of the transverse axis in a hyperbola's equation?

• The length of the transverse axis

• The value of the center

• The sign between the x-part and y-part

• The coefficients of x and y

Which hyperbola has a vertical transverse axis and a center at (2, 1)?

• None of the above

• Hyperbola A

• Hyperbola B

• Hyperbola C

What is the center of hyperbola B?

• (2, -1)

• (2, 1)

• (1, 2)

• (0, 0)

How do you transform an equation into standard form?

• Add the x-part and y-part

• Subtract the x-part from the y-part

• Multiply both sides by 2

• Ensure the right side equals 1

Which graph corresponds to the first equation after transformation?

• Graph B

• None of the above

• Graph C

• Graph A

What indicates a horizontal transverse axis in an equation?

• Negative center values

• Equal x and y coefficients

• y-part minus x-part

• x-part minus y-part

Which graph matches the second equation?

• None of the above

• Graph C

• Graph B

• Graph A

What is the center of the hyperbola in the second equation?

• (1, 2)

• (2, 1)

• (2, -1)

• (0, 0)

What is the transverse axis orientation for the third equation?

• Horizontal

• Vertical

• Diagonal

• None

Which graph corresponds to the third equation?

• Graph C

• None of the above

• Graph B

• Graph A