Mastering the Technique of Completing the Square

What is the first step in finding the equation of a circle by completing the square?

• Isolate the constant term

• Isolate the x and y terms

• Factor the equation

• Find the radius

When isolating x and y terms, what should you do to both sides of the equation?

• Add the same value

• Subtract the same value

• Multiply by the same value

• Divide by the same value

What do you do with the middle value of the x or y term when completing the square?

• Double it

• Square it

• Take half and square it

• Take the square root

Why do you need to add the same value to both sides of the equation when completing the square?

• To isolate the constant term

• To keep the equation balanced

• To find the radius

• To simplify the equation

What is the result of factoring the trinomial x^2 - 4x + 4?

• (x - 4)^2

• (x + 2)^2

• (x - 2)^2

• (x - 2)(x + 2)

How do you determine the center of the circle from the completed square form?

• By doubling the values inside the parentheses

• By taking the square root of the constant term

• By finding the constant term

• By using the values inside the parentheses

What is the radius of a circle if the equation is (x - 2)^2 + (y - 3)^2 = 25?

• 5

• 25

• 2

• 3

In the example x^2 + 12x + y^2 - 2y = 27, what value is added to complete the square for the x terms?

• 12

• 6

• 36

• 18

In the same example, what value is added to complete the square for the y terms?

• 2

• 4

• 1

• 9

What is the center of the circle for the equation (x + 5)^2 + (y - 3)^2 = 36?

• (5, 3)

• (5, -3)

• (-5, -3)

• (-5, 3)