document.write( "Question 459427: still stuck, please help\r
\n" ); document.write( "\n" ); document.write( "Find the quadratic equation that fits the following set of data points
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\n" ); document.write( "\n" ); document.write( "A classmate of mine had a question similar to this and got this answer:\r
\n" ); document.write( "\n" ); document.write( "8x^2 + 8x-7, could that be correct?
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Algebra.Com's Answer #315042 by Edwin McCravy(20056)\"\" \"About 
You can put this solution on YOUR website!
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document.write( "{(-5,124),(4,25),(-3,60)}\r\n" );
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document.write( "The general quadratic equation is\r\n" );
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document.write( "           y = Ax² + Bx + C\r\n" );
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document.write( "Plug in x = -5, y = 124 into\r\n" );
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document.write( "           y = Ax² + Bx + C\r\n" );
document.write( "         124 = A(-5)² + B(-5) + C\r\n" );
document.write( "         124 = A(25) - 5B + C\r\n" );
document.write( "         124 = 25A - 5B + C\r\n" );
document.write( "25A - 5B + C = 124\r\n" );
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document.write( "Plug in x = 4, y = 25 into\r\n" );
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document.write( "           y = Ax² + Bx + C\r\n" );
document.write( "          25 = A(4)² + B(4) + C\r\n" );
document.write( "          25 = A(16) + 4B + C\r\n" );
document.write( "          25 = 16A + 4B + C\r\n" );
document.write( "16A + 4B + C = 25\r\n" );
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document.write( "Plug in x = -3, y = 60 into\r\n" );
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document.write( "           y = Ax² + Bx + C\r\n" );
document.write( "          60 = A(-3)² + B(-3) + C\r\n" );
document.write( "          60 = A(9) - 3B + C\r\n" );
document.write( "          60 = 9A - 3B + C\r\n" );
document.write( " 9A - 3B + C = 60\r\n" );
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document.write( "Now we have this system of 3 equations in 3 unknowns:\r\n" );
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document.write( "25A - 5B + C = 124\r\n" );
document.write( "16A + 4B + C = 25\r\n" );
document.write( " 9A - 3B + C = 60\r\n" );
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document.write( "To eliminate C from the 1st 2 equations,\r\n" );
document.write( "multiply the 2nd eq. by -1\r\n" );
document.write( "and add to the 1st:\r\n" );
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document.write( " 25A - 5B + C = 124\r\n" );
document.write( "-16A - 4B - C = -25\r\n" );
document.write( "-------------------\r\n" );
document.write( "  9A - 9B     = 99\r\n" );
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document.write( "Divide that through by 9:\r\n" );
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document.write( "     A - B = 11 \r\n" );
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document.write( "16A + 4B + C = 25\r\n" );
document.write( " 9A - 3B + C = 60\r\n" );
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document.write( "To eliminate C from the 2nd and 3rd\r\n" );
document.write( "equations, multiply the 3rd eq. by -1\r\n" );
document.write( "and add to the 2nd:\r\n" );
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document.write( "16A + 4B + C =  25\r\n" );
document.write( "-9A + 3B - C = -60\r\n" );
document.write( "------------------\r\n" );
document.write( " 7A + 7B     = -35\r\n" );
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document.write( "Divide that through by 7\r\n" );
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document.write( "  A + B = -5\r\n" );
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document.write( "Now we have this system,\r\n" );
document.write( "which we add directly:\r\n" );
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document.write( "  A - B = 11 \r\n" );
document.write( "  A + B = -5\r\n" );
document.write( " -----------\r\n" );
document.write( " 2A     =  6\r\n" );
document.write( "      A = 3\r\n" );
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document.write( "Substitute in \r\n" );
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document.write( "  A + B = -5\r\n" );
document.write( "  3 + B = -5\r\n" );
document.write( "      B = -8\r\n" );
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document.write( "Substitute in \r\n" );
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document.write( "     9A - 3B + C = 60\r\n" );
document.write( "9(3) - 3(-8) + C = 60\r\n" );
document.write( "     27 + 24 + C = 60\r\n" );
document.write( "          51 + C = 60\r\n" );
document.write( "               C = 9\r\n" );
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document.write( "So\r\n" );
document.write( "           y = Ax² + Bx + C\r\n" );
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document.write( "becomes\r\n" );
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document.write( "           y = 3x² - 8x + 9\r\n" );
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document.write( "Edwin
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