Completing the Square Techniques

The video tutorial explains how to transform a quadratic expression into a completed square form. It begins with an introduction to the quadratic expression x squared plus 16x plus 9, emphasizing the importance of completing the square as a valuable algebraic technique. The process involves expanding the expression, identifying the value of 'a', and manipulating the expression by adding and subtracting 64 to maintain its value. The tutorial concludes by finalizing the expression into the form of x plus 8 squared minus 55, demonstrating the completion of the square.

Why is completing the square an important technique in algebra?

• It is only useful for graphing functions.

• It simplifies multiplication of polynomials.

• It is used to prove the quadratic formula.

• It helps in solving linear equations.

What is the expanded form of (x + a)^2?

• x^2 + 2ax + 2a

• x^2 + 2a + a^2

• x^2 + ax + a^2

• x^2 + 2ax + a^2

In the expression x^2 + 16x + 9, what is the value of 'a' when completing the square?

• 8

• 9

• 4

• 16

What value is added and subtracted to complete the square for x^2 + 16x + 9?

• 32

• 64

• 8

• 16

After completing the square, what is the expression x^2 + 16x + 9 rewritten as?

• (x + 4)^2 + 55

• (x + 8)^2 + 55

• (x + 8)^2 - 55

• (x + 4)^2 - 55

What is the constant term left after completing the square for x^2 + 16x + 9?

• 64

• 55

• -55

• -64