document.write( "Question 1193889: Find the quadratic function that fits the data points (1,6) (-1,2) and (3,34). \n" ); document.write( "
Algebra.Com's Answer #825991 by MathTherapy(10552)\"\" \"About 
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Find the quadratic function that fits the data points (1,6) (-1,2) and (3,34).
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Equation of a PARABOLA: y = ax2 + bx + c\r\n" );
document.write( "                        6 = a(1)2 + b(1) + c ----- Substituting (1, 6) for (x, y) \r\n" );
document.write( "                        6 = a + b + c ---- eq (i)\r\n" );
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document.write( "                        y = ax2 + bx + c\r\n" );
document.write( "                        2 = a(- 1)2 + b(- 1) + c ----- Substituting (- 1, 2) for (x, y) \r\n" );
document.write( "                        2 = a - b + c ---- eq (ii)\r\n" );
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document.write( "                        y = ax2 + bx + c\r\n" );
document.write( "                       34 = a(3)2 + b(3) + c ----- Substituting (3, 34) for (x, y) \r\n" );
document.write( "                       34 = 9a + 3b + c ---- eq (iii)\r\n" );
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document.write( "                          6 = a + b + c ------ eq (i)\r\n" );
document.write( "                          2 = a - b + c ------ eq (ii)\r\n" );
document.write( "                         34 = 9a + 3b + c --- eq (iii)\r\n" );
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document.write( "                          4 = 2b ---- Subtracting eq (ii) from eq (i)\r\n" );
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document.write( "                         32 = 8a + 4b ----- Subtracting eq (ii) from eq (iii) ---- eq (iv)\r\n" );
document.write( "                         32 = 8a + 4(2) --- Substituting 2 for b in eq (iv)\r\n" );
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document.write( "                          6 = 3 + 2 + c ---- Substituting 3 for a, and 2 for b in eq (i)\r\n" );
document.write( "                          6 = 5 + c \r\n" );
document.write( "                          1 = c \r\n" );
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document.write( "  Equation of a PARABOLA: y = ax2 + bx + c\r\n" );
document.write( "                          y = 3x2 + 2x + 1 ------- Substituting 3 for a, 2 for b, and 1 for c
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