Completing the Square: Using an Area Model to Rewrite Quadratic Expressions

This video tutorial explains how to complete the square in a quadratic expression using an area model. It begins by defining perfect squares and illustrating them with examples. The tutorial then introduces the concept of using area blocks to represent polynomials, detailing the different types of blocks used. The main focus is on completing the square for the expression x-squared plus 6x, demonstrating how to arrange area blocks to form a perfect square. The tutorial concludes by showing how to express the original polynomial in vertex form, emphasizing the importance of understanding perfect squares in quadratic expressions.

What is a perfect square in mathematical terms?

• A number divided by itself

• A number subtracted from itself

• A number added to itself

• A number or expression multiplied by itself

Which of the following is a perfect square trinomial?

• x-squared plus 5x plus 6

• x-squared plus 4x plus 3

• x-squared plus 2x plus 1

• x-squared plus 6x plus 9

What is required for a polynomial to be considered a perfect square?

• It must have a constant term

• It must be factorable into two identical factors

• It must have three terms

• It must have a linear term

What is the area of a block that measures x units by x units?

• x-squared units

• x plus 1 units

• x units

• 2x units

How many 'long' blocks are used to represent the term 6x?

• 6

• 9

• 3

• 2

What additional blocks are needed to complete the square for x-squared plus 6x?

• 6 unit blocks

• 4 unit blocks

• 9 unit blocks

• 12 unit blocks

What is the vertex form of the expression x-squared plus 6x?

• x plus 3 quantity squared plus 9

• x plus 3 quantity squared minus 9

• x plus 2 quantity squared minus 4

• x plus 2 quantity squared plus 4