document.write( "Question 642920: Write a function rule for the table.
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Algebra.Com's Answer #404285 by Edwin McCravy(20055)\"\" \"About 
You can put this solution on YOUR website!
We graph those 4 points: (0,3), (1,4), (2,5), (3,0)\r\n" );
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document.write( "Its graph cannot be a second degree quadratic function (parabola) \r\n" );
document.write( "because it has three points in a straight line.\r\n" );
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document.write( "Since it goes through the point (3,0) The equation must\r\n" );
document.write( "have (x - 3) as a factor.\r\n" );
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document.write( "So perhaps its equation is  F(x) = the product of (x-3) and a\r\n" );
document.write( "quadratic, like this:\r\n" );
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document.write( "   F(x) = y = (x - 3)(Ax² + Bx + C)\r\n" );
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document.write( "We know it has y-intercept (0,3) so we can substitute that and get\r\n" );
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document.write( "          3 = (0 - 3)(A·0² _ B·0 + C)\r\n" );
document.write( "          3 = -3C\r\n" );
document.write( "         -1 = C\r\n" );
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document.write( "So wesubstitute that and we have:\r\n" );
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document.write( "   F(x) = y = (x - 3)(Ax² + Bx - 1) \r\n" );
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document.write( "We substitute (1,4)\r\n" );
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document.write( "          4 = (1 - 3)(A·1² + B·1 - 1)\r\n" );
document.write( "          4 = -2(A + B - 1)\r\n" );
document.write( "          4 = -2A - 2B + 2\r\n" );
document.write( "    2A + 2B = -2\r\n" );
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document.write( "Divide through by 2\r\n" );
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document.write( "      A + B = -1\r\n" );
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document.write( "We substitute (2,5)\r\n" );
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document.write( "          5 = (2 - 3)(A·2² + B·2 - 1)\r\n" );
document.write( "          5 = -1(4A + 2B - 1)\r\n" );
document.write( "          5 = -4A - 2B + 1\r\n" );
document.write( "    4A + 2B = -4\r\n" );
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document.write( "Divide through by 2\r\n" );
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document.write( "     2A + B = -2\r\n" );
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document.write( "So we solve the system of equations:\r\n" );
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document.write( "      A + B = -1\r\n" );
document.write( "     2A + B = -2\r\n" );
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document.write( "and get A = -1 and B = 0\r\n" );
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document.write( "So the function is\r\n" );
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document.write( "   F(x) = (x - 3)(-1x² + 0x - 1)\r\n" );
document.write( "   F(x) = (x - 3)(-x² - 1)\r\n" );
document.write( "   F(x) = (x - 3)(-1)(x² + 1)\r\n" );
document.write( "   F(x) = -(x-3)(x²+1)\r\n" );
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document.write( "and its graph is:\r\n" );
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document.write( "Edwin
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