Once we hit the x intercept at x 0 we know that weve

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Unformatted text preview: se it. This process assumes that all the zeroes are real numbers. If there are any complex zeroes then this process may miss some pretty important features of the graph. Let’s sketch a couple of polynomials. Example 1 Sketch the graph of P ( x ) = 5 x5 - 20 x 4 + 5 x3 + 50 x 2 - 20 x - 40 . Solution We found the zeroes and multiplicities of this polynomial in the previous section so we’ll just write them back down here for reference purposes. x = -1 ( multiplicity 2 ) x=2 ( multiplicity 3) So, from the fact we know that x = -1 will just touch the x-axis and not actually cross it and that x = 2 will cross the x-axis and will be flat as it does this since the multiplicity is greater than 1. Next, the y-intercept is ( 0, -40 ) . The coefficient of the 5th degree term is positive and since the degree is odd we know that this polynomial will increase without bound at the right end and decrease without bound at the left end. Finally, we just need to evaluate the polynomial at a couple of points. The po...
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This note was uploaded on 06/06/2012 for the course ICT 4 taught by Professor Mrvinh during the Spring '12 term at Hanoi University of Technology.

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