Finding the Center and Radius of a Circle through Completing the Square

Mrs. Gala introduces the concept of completing the square, a technique learned in Algebra 1, and its application in geometry to find the center and radius of a circle. The video reviews expanding trinomials, creating perfect squares, and applying these concepts to solve circle equations. The lesson emphasizes understanding the relationship between numbers in trinomials and their expanded forms, and how to use this knowledge to complete the square for both algebraic and geometric purposes.

What is the primary use of completing the square in geometry?

• To compute the perimeter of rectangles

• To calculate the area of triangles

• To identify the center and radius of a circle

• To determine the angles in polygons

What does the expression (X - 5)^2 expand to?

• X^2 - 5X + 25

• X^2 - 25

• X^2 + 10X + 25

• X^2 - 10X + 25

How do you find the number to complete the square in the expression X^2 + 6X + ___?

• Divide the coefficient of X by 2 and square it

• Square the coefficient of X and divide by 2

• Multiply the coefficient of X by 2 and add 1

• Add 1 to the coefficient of X and square the result

What is the completed square form of X^2 + 6X + 9?

• (X - 4.5)^2

• (X + 3)^2

• (X + 4.5)^2

• (X - 3)^2

What values of X complete the square for the trinomial X^2 - 6X + 9?

• X + 3

• X - 3

• X + 6

• X - 6

Given the equation X^2 + 4X + 4, what is the factored form?

• (X - 4)^2

• (X + 4)^2

• (X - 2)^2

• (X + 2)^2

In the context of circles, what does completing the square help to determine?

• Area and diameter

• Diameter and circumference

• Circumference and area

• Center and radius

For the equation Y^2 - 12Y + 36, what is the correct factored form?

• (Y + 12)^2

• (Y - 12)^2

• (Y + 6)^2

• (Y - 6)^2

What is the center of a circle if the completed square form of its equation is (X + 2)^2 + (Y - 6)^2 = 81?

• (-2, -6)

• (2, -6)

• (-2, 6)

• (2, 6)

What is the radius of the circle if its equation is (X + 2)^2 + (Y - 6)^2 = 81?

• 18

• 81

• 3

• 9