Completing the Square with Algebra Tiles

Miss Pierce introduces the concept of completing the square, focusing on perfect squares and their properties. She explains how to factor trinomials into perfect squares and engages students in a game to find constants in trinomials. The lesson concludes with a demonstration of completing the square using algebra tiles, providing a visual and interactive approach to understanding the topic.

What is a perfect square trinomial?

• A trinomial that can be factored into identical binomials

• A trinomial that cannot be factored

• A trinomial with no real roots

• A trinomial derived from a quadratic equation

What does the expression x^2 - 22x + 121 simplify to?

• x(x - 22) + 121

• None of the above

• (x - 11)^2

• (x + 11)^2

Which pair of factors correctly factors the trinomial x^2 + 8x + 16?

• (x + 4)(x + 4)

• (x - 4)(x - 4)

• (x + 8)(x + 2)

• (x - 8)(x - 2)

What constant completes the square for the trinomial x^2 + 12x?

• 36

• 144

• 72

• 12

What constant completes the square for the trinomial x^2 + 14x?

• 49

• 196

• 7

• 28

What constant completes the square for the trinomial x^2 - 20x?

• 100

• 10

• 20

• 400

What constant completes the square for the trinomial x^2 - 6x?

• 9

• 36

• 3

• 18

How do you complete the square using algebra tiles for the polynomial x^2 + 6x + 17?

• Rearrange to form (x + 3)^2 - 8

• Rearrange to form (x - 3)^2 - 8

• Rearrange to form (x + 3)^2 + 8

• Rearrange to form (x - 3)^2 + 8

What is the final expression when completing the square for x^2 + 6x + 17?

• (x - 3)^2 - 8

• (x - 3)^2 + 8

• (x + 3)^2 - 8

• (x + 3)^2 + 8

What does completing the square help to achieve in algebra?

• All of the above

• Solving quadratic equations

• Factoring trinomials into binomials

• Simplifying expressions to reveal perfect squares