document.write( "Question 208402: Find an equation for the points (1,1) (2,3) (3,6) and (4, 10). \n" ); document.write( "
Algebra.Com's Answer #157627 by Edwin McCravy(20056)\"\" \"About 
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Edwin's solution:
\n" ); document.write( "Find an equation for the points (1,1) (2,3) (3,6) and (4, 10)
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document.write( "Put down the y values in a row:\r\n" );
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document.write( "   1   3   6   10\r\n" );
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document.write( "Find the first successive differences by subtracting \r\n" );
document.write( "neighboring numbers, and write their differences \r\n" );
document.write( "between and below them:\r\n" );
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document.write( "   1   3   6   10\r\n" );
document.write( "     2   3   4\r\n" );
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document.write( "Find the second successive differences again by \r\n" );
document.write( "subtracting neighboring numbers, and writing their \r\n" );
document.write( "differences between and below them:\r\n" );
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document.write( "   1   3   6   10\r\n" );
document.write( "     2   3   4\r\n" );
document.write( "       1   1\r\n" );
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document.write( "That took 2 lines of differences until all the differences\r\n" );
document.write( "were all the same, in this case, 1. \r\n" );
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document.write( "So we know that we need an equation of degree 2.\r\n" );
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document.write( "\"Ax%5E2%2BBx%2BC=y\"\r\n" );
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document.write( "Plug in all three points:\r\n" );
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document.write( "Plug in (1,1) \r\n" );
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document.write( "\"A%281%29%5E2%2BB%281%29%2BC=1\"\r\n" );
document.write( "\"A%2BB%2BC=1\"\r\n" );
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document.write( "Plug in (2,3) \r\n" );
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document.write( "\"A%282%29%5E2%2BB%282%29%2BC=3\"\r\n" );
document.write( "\"4A%2B2B%2BC=3\"\r\n" );
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document.write( "Plug in (3,6) \r\n" );
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document.write( "\"A%283%29%5E2%2BB%283%29%2BC=6\"\r\n" );
document.write( "\"9A%2B3B%2BC=6\"\r\n" );
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document.write( "You don't need the fourth point.\r\n" );
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document.write( "So you have the system:\r\n" );
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document.write( "\"system%28A%2BB%2BC=1%2C4A%2B2B%2BC=3%2C9A%2B3B%2BC=6%29\"\r\n" );
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document.write( "Solve that system and get:\r\n" );
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document.write( "\"A=1%2F2\", \"B=1%2F2\" and \"C=0\"\r\n" );
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document.write( "Therefore:\r\n" );
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document.write( "\"Ax%5E2%2BBx%2BC=y\"\r\n" );
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document.write( "becomes:\r\n" );
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document.write( "\"%281%2F2%29x%5E2%2B%281%2F2%29x%2B%280%29=y\"\r\n" );
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document.write( "or\r\n" );
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document.write( "\"y=%281%2F2%29x%5E2%2B%281%2F2%29x\"\r\n" );
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document.write( "Factor out \"%281%2F2%29x\" on the right:\r\n" );
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document.write( "\"y=%281%2F2%29x%28x%2B1%29\"\r\n" );
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document.write( "To take \"1%2F2\" is the same as dividing by \"2\":\r\n" );
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document.write( "\"y=%28x%28x%2B1%29%29%2F2\"\r\n" );
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document.write( "Edwin

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