How to write a hyperbola in vertex form and determine the center, vertices and foci

The video tutorial covers the process of solving equations by grouping terms, completing the square, and rewriting equations. It highlights common mistakes students make and explains how to identify the type of graph, its orientation, and center. The tutorial focuses on hyperbolas, detailing how to find vertices and foci, and emphasizes the importance of understanding the horizontal transverse axis.

What is the first step in solving equations by completing the square?

• Grouping the constants

• Grouping the x's and y's

• Factoring out the coefficient of y^2

• Adding constants to both sides

How do you create a perfect square trinomial?

• Add b to both sides

• Divide b by 2 and square it

• Multiply b by 2 and square it

• Subtract b from both sides

Why is it important to add the squared values correctly to both sides of the equation?

• To ensure the equation remains balanced

• To eliminate the constants

• To factor the equation

• To simplify the equation

What is the equation for a hyperbola after simplifying?

• x^2 + y^2 = 1

• x^2 - y^2 = 1

• x^2 + y^2 = 0

• x^2 - y^2 = 0

How do you determine the orientation of the transverse axis of a hyperbola?

• By observing the subtraction between terms

• By identifying the larger coefficient

• By calculating the distance between vertices

• By checking if the equation is equal to zero

What is the center of the hyperbola in the given example?

• (-2, 1)

• (2, -1)

• (1, 2)

• (0, 0)

Which axis do the vertices and foci of the hyperbola lie on?

• Diagonal axis

• Vertical axis

• None of the above

• Horizontal axis