A hands on approach to completing the square Completing the Square with Algebra Tiles.

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Presentation transcript:

A hands on approach to completing the square Completing the Square with Algebra Tiles

Completing the Square 2 Algebra tiles can be used to complete the square Use tiles and frame to represent problem. The expression should form a square array inside the frame. The square factors will form the dimensions Be prepared to use zero pairs of constants to complete the square

Rewrite as a binomial squared 3 x 2 + 4x Determine and model the dimensions of the square Model the expression Arrange the tiles so they start to form a square. x 2 + 4x+4 = Determine how many 1’s you have to add to make it a square Ex: Complete the square for

Rewrite as a binomial squared 4 x 2 – 6 x Determine and model the dimensions of the square Model the expression Arrange the tiles so they start to form a square. x 2 – 6x+9 = Determine how many 1’s you have to add to make it a square Ex: Complete the square for

You try

Patterns What patterns have you noticed? What did you do with the x terms in order to make a square? What pattern did you see for adding your constant term? How is your constant term related to your middle term?

Solving Equations by completing the square We will complete the square on one side of the equation. Remember that whatever we add to one side of the equation, we must add to the other. Then re-write our perfect square trinomial as the sum/difference of a binomial. Use the Square Root Method to solve for x !

Ex: Solve First, model the equation. Next, arrange the left side to form a square Complete the square by adding 1’s Add to both sides Rewrite each side Write as the sum of a binomial Take the square root of each side

Ex: Solve First, model the equation. Next, arrange the left side to form a square Complete the square by adding 1’s Add to both sides Rewrite each side Write as the sum of a binomial Take the square root of each side

You try