Section 2: Vertex Form

Elementary and Intermediate Algebra: Graphs & Models (3rd Edition)

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442 Chapter 5 Quadratic Functions Version: Fall 2007 l⚏ Example 5. Expand ( x + 4) 2 . We could proceed as follows. ( x + 4) 2 = ( x + 4)( x + 4) = x ( x + 4) + 4( x + 4) = x 2 + 4 x + 4 x + 16 = x 2 + 8 x + 16 Although correct, this technique will not help us with our upcoming task. What we need to do is follow the algorithm suggested by Property 3 . Algorithm for Squaring a Binomial. To square the binomial a + b , proceed as follows: 1. Square the first term to get a 2 . 2. Multiply the first and second terms together, and then multiply the result by two to get 2 ab . 3. Square the second term to get b 2 . Thus, to expand ( x + 4) 2 , we should proceed as follows. 1. Square the first term to get x 2 2. Multiply the first and second terms together and then multiply by two to get 8 x . 3. Square the second term to get 16 . Proceeding in this manner allows us to perform the expansion mentally and simply write down the solution. ( x + 4) 2 = x 2 + 2( x )(4) + 4 2 = x 2 + 8 x + 16 Here are a few more examples. In each, we’ve written an extra step to help clarify the procedure. In practice, you should simply write down the solution without any intermediate steps.
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