Completing the Square Concepts

This video tutorial teaches how to transform quadratic equations by completing the square using a model. It explains the values of different model pieces and demonstrates how to build a square with them. The tutorial provides examples of completing the square for quadratic equations like x squared plus 6x and x squared plus 8x, showing the transformation process and the resulting equivalent equations.

What is the value of the long green bar in the model?

• 1

• x

• -1

• -x

What are the dimensions of the square built from x^2 + 4x + 4?

• x + 1 by x + 1

• x + 2 by x + 2

• x + 3 by x + 3

• x + 4 by x + 4

What is a common misunderstanding about x times x?

• x times x is x^2

• x times x is 2x

• x times x is x

• x times x is 0

What is the equivalent expression for x^2 + 6x + 9?

• (x + 5)^2

• (x + 4)^2

• (x + 3)^2

• (x + 2)^2

What is the result of x times 3 in the context of completing the square?

• 3x

• x^2

• 6x

• 9

How many additional ones are needed to complete the square for x^2 + 8x + 7?

• 7

• 8

• 10

• 9

What is the completed square form of x^2 + 8x + 16?

• (x + 3)^2

• (x + 4)^2

• (x + 5)^2

• (x + 6)^2

What transformation occurs when completing the square for x^2 + 8x + 7?

• The equation becomes x^2 + 8x + 7

• The equation becomes x^2 + 8x + 8

• The equation becomes x^2 + 8x + 16

• The equation becomes x^2 + 8x + 9

What is the final form of the equation after completing the square for x^2 + 8x + 7?

• (x + 3)^2

• x^2 + 8x + 7

• (x + 4)^2

• (x + 4)^2 - 9

What is the purpose of completing the square in quadratic equations?

• To factor the equation

• To simplify the equation

• To solve the equation

• To transform the equation