Completing the Square and Circles

The video tutorial covers completing the square to find the center and radius of a circle, using example problems to illustrate the process. It also includes exercises on matching expressions to form perfect square trinomials, finding the center and radius from equations, and factoring into squared binomials. Additionally, the tutorial explains how to apply the distributive property to rearrange circle equations, graph a circle, and compare the surface area to volume ratio of a cube and a sphere.

What is the first step in completing the square to find the center of a circle?

• Multiply the middle term by two.

• Subtract the constant term from both sides.

• Divide the middle term by two.

• Add the constant term to both sides.

After dividing the middle term by two in completing the square, what should you do next?

• Add the result to both sides.

• Square the result.

• Multiply the result by the constant term.

• Subtract the result from both sides.

How do you determine the radius of a circle after completing the square?

• Multiply the constant term by two.

• Add all terms and take the square root.

• Take the square root of the constant term.

• Divide the constant term by two.

What is the value needed to complete the square for the expression x^2 + 8x?

• 64

• 16

• 4

• 8

Which expression matches with the value 100 to form a perfect square trinomial?

• x^2 + 20x

• x^2 + 10x

• x^2 + 25x

• x^2 + 5x

What is the center of the circle represented by the equation (x+2)^2 + (y-5)^2 = 9?

• (2, -5)

• (5, -2)

• (-2, 5)

• (-5, 2)

How do you rearrange terms to find the center and radius of a circle from an equation?

• Multiply x and y terms.

• Group x and y terms separately.

• Add all terms together.

• Subtract y terms from x terms.

Which expression can be factored into a squared binomial?

• x^2 + 7x + 12

• x^2 + 4x + 4

• x^2 + 5x + 10

• x^2 + 6x + 8

What is the result of applying the distributive property to (x+3)^2?

• x^2 + 6x + 9

• x^2 + 9x + 9

• x^2 + 3x + 3

• x^2 + 3x + 9

How do you rearrange the equation x^2 + 6x + y^2 - 18y + 65 = 0 to find the center?

• Multiply x and y terms.

• Subtract y terms from x terms.

• Add all terms together.

• Complete the square for x and y terms.