Learn how to sketch the graph of a hyperbola in general form

The video tutorial explains how to rewrite an equation in standard form by completing the square. It covers the process of grouping terms, factoring, and creating perfect square trinomials. The tutorial also demonstrates how to identify key features such as the center and axes, and how to graph the equation. Corrections and clarifications are provided throughout to ensure understanding.

What is the first step in rewriting an equation into standard form?

• Multiply by 9

• Add 4 to both sides

• Subtract 4 from both sides

• Group the x and y terms

Why is it necessary to factor out coefficients before completing the square?

• To ensure the coefficient of the squared term is one

• To simplify the equation

• To eliminate the constant term

• To make the equation more complex

How do you find the value that completes the square?

• Divide the middle term by 2 and square it

• Subtract the middle term from itself

• Add the middle term to itself

• Multiply the middle term by 2 and square it

What is the relationship between a squared and b squared in determining the major axis?

• b squared is always larger than a squared

• a squared is always larger than b squared

• b squared is in front and determines the axis

• a squared is in front and determines the axis

What is the center of the equation after transforming it into standard form?

• (1, 2)

• (2, -1)

• (2, 1)

• (0, 0)

How are the vertices determined in relation to the center?

• By adding and subtracting the value of a from the x-coordinate

• By dividing the y-coordinate by b

• By adding and subtracting the value of b from the y-coordinate

• By multiplying the x-coordinate by a

What is the equation for the asymptotes in a horizontal transverse axis?

• y = ± b/a * (y - k) + h

• y = ± a/b * (x - h) + k

• y = ± b/a * (x - h) + k

• y = ± a/b * (y - k) + h