document.write( "Question 369474: I need help with sketching the graph of this factored polynomial
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Algebra.Com's Answer #263287 by Edwin McCravy(20055)\"\" \"About 
You can put this solution on YOUR website!
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document.write( "I need help with sketching the graph of this factored polynomial \r\n" );
document.write( "\"y=%28x%2B1%29%5E4+%28x-2%29%5E3+%28x-1%29\"\r\n" );
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document.write( "The roots, zeros, x-intercepts, or solutions \r\n" );
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document.write( "(they are called by all four names at different times and are the\r\n" );
document.write( "places where the curve comes in contact with the x-axis) \r\n" );
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document.write( "are found by setting the expressions in the parentheses = 0\r\n" );
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document.write( "x+1=0, x-2=0, x-1=0\r\n" );
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document.write( "and solving, getting\r\n" );
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document.write( "x=-1, x=2, and x=1\r\n" );
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document.write( "When you have something like this:  \"%28x-R%29%5EN\" as a factor\r\n" );
document.write( "of a polynomial then we say R is a zero with multiplicity of N.  \r\n" );
document.write( "If N is an even number the graphed curve \"bounces\" off the x-axis \r\n" );
document.write( "at R, and if N  is an odd number, the graphed curve cuts through \r\n" );
document.write( "the x-axis at R.\r\n" );
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document.write( "Since the exponent 4 in \"%28x%2B1%29%5E4\" is even, we know that the \r\n" );
document.write( "graphed curve \"bounces off\" the x-axis at -1.\r\n" );
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document.write( "Since the exponent 3 in \"%28x-2%29%5E3\" is odd, we know that the \r\n" );
document.write( "graphed curve cuts through the x-axis at 2.\r\n" );
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document.write( "Since the understood exponent 1 in \"%28x-1%29\" is odd, we know that the \r\n" );
document.write( "graphed curve cuts through the x-axis at 1.\r\n" );
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document.write( "The y-intercept is found by substituting 0 for x in\r\n" );
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document.write( "\"y=%280%2B1%29%5E4+%280-2%29%5E3+%280-1%29\"\r\n" );
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document.write( "\"y=%281%29%5E4%28-2%29%5E3+%28-1%29\"\r\n" );
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document.write( "\"y=%281%29%28-8%29%28-1%29\"\r\n" );
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document.write( "\"y=8\"\r\n" );
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document.write( "So we draw the graph this way.  We start at the y-intercept and draw\r\n" );
document.write( "downward to the left so that the curve bounces off the x-axis at -1.\r\n" );
document.write( "Then to the right it eventually goes down and cuts through the x-axis\r\n" );
document.write( "at 1 and 2. \r\n" );
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document.write( "Here is the graph\r\n" );
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document.write( "\"graph%284000%2F17%2C800%2C-2%2C3%2C-5%2C12%2C%28x%2B1%29%5E4+%28x-2%29%5E3+%28x-1%29%29\"\r\n" );
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document.write( "The graph cuts through the x-axis at 1 and 2 and \"bounces off\" the \r\n" );
document.write( "x-axis at -1.  To draw it accurately like this you would\r\n" );
document.write( "have to plot some more points.\r\n" );
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document.write( "Edwin
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