Presentation1.pptx perfect square trinomial

trinomial

1. What does a square look like? Is this a square? What about this one? This one? Why isn’t the last picture a square? What would we need to do to make this a square?

2. We can model a quadratic expression like this x 2 + 4x + 4 with tiles like this

3. We are missing a space in our square. Illustrative Example: x 2 + 6x – 8 = 0 We will use algebra tiles to help us with the non factorable problem. The algebra tiles will help us get a new c value that will help us factor into a new perfect square. ax 2 + bx + c a= b = c = so for x 2 + 6x – 8 ; a = 1 b = 6 c = -8 using algebra tiles we have How many s would we really need to complete the square? Answer = 9 s

4. A. Complete the square of the following: 1. x² + 4x + _____ 2. x² – 6x + _____ 3. x² – 12 x +_____ 4. n² – 18n + _____ 5. x² + 8x + _____

5. B. Determine a number that must be added to both sides of each equation to complete the square? x 2 + 4x = 12 x 2 – 2x = 24 x 2 – 6x = -8 x 2 – 6x = 7 5. x 2 + 6x = 16

6. What does it mean to “complete the square”? How do you describe a perfect square trinomial? How can you determine a number that must be added to the terms of polynomial to make it a perfect square trinomial? Observe the terms of each trinomial. How is the third term related to the coefficient of the middle term?