document.write( "Question 407012: Write an equation to represent each relation, {(-6,4),(-3,8),(1,-24),(2,-12),(6,-4)} and {(-4,3),(-2,12),(-1,48),(1,48),(2,12)} \n" ); document.write( "
Algebra.Com's Answer #287028 by Edwin McCravy(20086)\"\" \"About 
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document.write( "{(-6,4),(-3,8),(1,-24),(2,-12),(6,-4)} \r\n" );
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document.write( "Assume a polynomial equation of one less degree than the number \r\n" );
document.write( "of points given.  There are 5 points given, so we assume a 4th \r\n" );
document.write( "degree equation:\r\n" );
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document.write( "\"y+=+Ax%5E4+%2B+Bx%5E3+%2B+Cx%5E2+%2B+Dx+%2B+E\"\r\n" );
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document.write( "Substituting each of the five given points into that equation:\r\n" );
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document.write( "\"4+=+A%28-6%29%5E4+%2B+B%28-6%29%5E3+%2B+C%28-6%29%5E2+%2B+D%28-6%29+%2B+E\"\r\n" );
document.write( "\"8+=+A%28-3%29%5E4+%2B+B%28-3%29%5E3+%2B+C%28-3%29%5E2+%2B+D%28-3%29+%2B+E\"\r\n" );
document.write( "\"-24+=+A%281%29%5E4+%2B+B%281%29%5E3+%2B+C%281%29%5E2+%2B+D%281%29+%2B+E\"\r\n" );
document.write( "\"-12+=+A%282%29%5E4+%2B+B%282%29%5E3+%2B+C%282%29%5E2+%2B+D%282%29+%2B+E%29+\"\r\n" );
document.write( "\"-4+=+A%286%29%5E4+%2B+B%286%29%5E3+%2B+C%286%29%5E2+%2B+D%286%29+%2B+E+\"\r\n" );
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document.write( "That becomes the system:\r\n" );
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document.write( "        \r\n" );
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document.write( "Solve that system of equations and get\r\n" );
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document.write( "\"A=-1%2F9\", \"B=0\", \"C=43%2F9\", \"D=-2%2F3\", \"E=-28\"\r\n" );
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document.write( "So the equation \r\n" );
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document.write( "\"y+=+Ax%5E4+%2B+Bx%5E3+%2B+Cx%5E2+%2B+Dx+%2B+E+\"\r\n" );
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document.write( "becomes\r\n" );
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document.write( "\"y+=+expr%28-1%2F9%29x%5E4+%2B+expr%2843%2F9%29x%5E2+-+expr%282%2F3%29x+-28\"\r\n" );
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document.write( "and the graph of it is:\r\n" );
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document.write( "-------------------\r\n" );
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document.write( "Your second problem is done the same way.  The answer is\r\n" );
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document.write( "\"y+=+expr%283%2F4%29x%5E4+-+expr%2863%2F4%29x%5E2+%2B63\"\r\n" );
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document.write( "Edwin

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