Completing the Square Using Algebra

This lesson teaches how to complete the square using algebra. It begins with a review of quadratic expressions and identifying the coefficients A, B, and C. The lesson then explains how to determine if an expression is a perfect square and how to factor it using a specific formula. The process of transforming quadratic equations by completing the square is demonstrated, including handling cases with negative B values. By the end, students should understand the steps to complete the square and factor quadratic equations effectively.

What are the values of A, B, and C in the expression X^2 - 6X + 9?

• A = 0, B = -6, C = 9

• A = 1, B = 6, C = -9

• A = 1, B = -6, C = 9

• A = 1, B = 6, C = 9

What is the first step in determining if a quadratic expression is a perfect square?

• Subtract the C term from both sides

• Divide the A term by 2

• Determine the values of A, B, and C

• Multiply the B term by 2

How do you factor a perfect square when A = 1?

• Use the formula X - B/2 * X - B/2

• Use the formula X^2 - B^2

• Use the formula X + B/2 * X + B/2

• Use the formula X^2 + B^2

What is the value of C when completing the square for the equation X^2 + 4X + C = 5?

• C = 2

• C = 16

• C = 4

• C = 8

After completing the square, what is the transformed equation of X^2 + 4X + 4 = 9?

• (X + 2)^2 = 9

• (X - 2)^2 = 9

• (X - 4)^2 = 9

• (X + 4)^2 = 9

In the equation X^2 - 4X - 1 = 0, what is the value of B/2?

• -2

• 4

• -4

• 2

What is the completed square form of X^2 - 4X + 4 = 5?

• (X + 4)^2 = 5

• (X + 2)^2 = 5

• (X - 2)^2 = 5

• (X - 4)^2 = 5