Alg_Complete

2007 paul dawkins 262

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Unformatted text preview: reasons for plotting points at the ends is to see just how fast the graph is increasing or decreasing. We can see from the evaluations that the graph is decreasing on the left end much faster than it’s increasing on the right end. Okay, let’s take a look at another polynomial. This time we’ll go all the way through the process of finding the zeroes. Example 2 Sketch the graph of P ( x ) = x 4 - x3 - 6 x 2 . Solution First, we’ll need to factor this polynomial as much as possible so we can identify the zeroes and get their multiplicities. P ( x ) = x 4 - x 3 - 6 x 2 = x 2 ( x 2 - x - 6 ) = x 2 ( x - 3) ( x + 2 ) Here is a list of the zeroes and their multiplicities. © 2007 Paul Dawkins 259 http://tutorial.math.lamar.edu/terms.aspx College Algebra x = -2 ( multiplicity 1) ( multiplicity 2 ) ( multiplicity 1) x=0 x=3 So, the zeroes at x = -2 and x = 3 will correspond to x-intercepts that cross the x-axis since their multiplicity is odd and will do so at an angle since their multiplicity is NOT at least 2. The zero at x = 0 will not cross the x-axis since its multiplicity is even. The y-intercept is ( 0, 0...
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