Understanding Completing the Square

This video tutorial covers the concept of completing the square, especially when the coefficient of x squared is not one. It uses area models and algebra tiles to represent expressions and find missing terms. The lesson includes practical examples from a quilt shop scenario, where orders are modeled as perfect squares. The video also discusses how to adjust expressions to match customer requirements, emphasizing the use of the greatest common factor and algebraic manipulation.

What is the main focus of the lesson on completing the square?

• Graphing quadratic functions

• Understanding expressions with a coefficient of x squared not equal to one

• Finding the roots of a polynomial

• Solving quadratic equations

How are expressions represented in the lesson using area models?

• As circles

• As triangles

• As squares

• As rectangles

In the example of 4x squared, how is the expression modeled?

• Using eight x squared areas

• Using six x squared areas

• Using four x squared areas

• Using two x squared areas

What is the missing value needed to complete the square for 2x squared plus 8x?

• 2

• 3

• 4

• 5

How many small squares are needed to complete the square for 3x squared plus 24x?

• 16

• 9

• 12

• 25

What is the greatest common factor used in the expression 2x squared plus 12x?

• 2

• 1

• 4

• 3

How is the expression 2x squared plus 12x plus 13 adjusted to form a perfect square?

• Subtract 5

• Add 5

• Add 9

• Subtract 9

What is the missing value to make 3x squared minus 30x a perfect square?

• 36

• 9

• 16

• 25

How is the expression 3x squared minus 30x rewritten as a perfect square?

• 3 times (X plus 10) squared

• 3 times (X minus 5) squared

• 3 times (X plus 5) squared

• 3 times (X minus 10) squared

What is the final expression for the area of 2x squared plus 12x plus 13?

• 2 times (X plus 3) squared minus 5

• 2 times (X minus 3) squared minus 5

• 2 times (X minus 3) squared plus 5

• 2 times (X plus 3) squared plus 5