document.write( "Question 1114193: Find the quadratic equation that fits the following set of data points.
\n" ); document.write( "(−2,−8),(−4,−12),(1,13)
\n" ); document.write( "f(x)=______.
\n" ); document.write( "(Use integers or fractions for any numbers in the expression. Do not factor.) \n" ); document.write( "

Algebra.Com's Answer #729215 by MathTherapy(10552) $\"\"$ $\"About$

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\n" ); document.write( "Find the quadratic equation that fits the following set of data points.
\n" ); document.write( "(−2,−8),(−4,−12),(1,13)
\n" ); document.write( "f(x)=______.
\n" ); document.write( "(Use integers or fractions for any numbers in the expression. Do not factor.)
\n" ); document.write( "

Standard equation of a quadratic function: \r\n" );
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document.write( "(− 2,− 8)\r\n" );
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document.write( " ------ Substituting (- 2, - 8) for (x, y)\r\n" );
document.write( "4a - 2b + c = - 8 ------- eq (i)\r\n" );
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document.write( "(− 4, − 12)\r\n" );
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document.write( " ------ Substituting (- 4, - 12) for (x, y)\r\n" );
document.write( "16a - 4b + c = - 12 ------- eq (ii)\r\n" );
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document.write( "(1, 13)\r\n" );
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document.write( " ------ Substituting (1, 13) for (x, y)\r\n" );
document.write( "a + b + c = 13 ------- eq (iii)\r\n" );
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document.write( " 4a - 2b + c = -  8 ------- eq (i)\r\n" );
document.write( "16a - 4b + c = - 12 ------- eq (ii)\r\n" );
document.write( "  a +  b + c =   13 ------- eq (iii)\r\n" );
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document.write( "12a - 2b = - 4 ------ Subtracting eq (i) from eq (ii) \r\n" );
document.write( "2(6a - b) = 2(- 2) \r\n" );
document.write( "6a - b = - 2 ------ eq (iv)\r\n" );
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document.write( "3a - 3b = - 21 ------ Subtracting eq (iii) from eq (i) \r\n" );
document.write( "3(a - b) = 3(- 7) \r\n" );
document.write( "a - b = - 7 ------ eq (v)\r\n" );
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document.write( "5a = 5 ------- Subtracting eq (v) from eq (iv)\r\n" );
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document.write( "1 - b = - 7 ------- Substituting 1 for a in eq (v)\r\n" );
document.write( "- b = - 7 - 1\r\n" );
document.write( "- b = - 8\r\n" );
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document.write( "1 + 8 + c = 13 ------- Substituting 1 for a, and 8 for b in eq (iii)\r\n" );
document.write( "9 + c = 13\r\n" );
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document.write( " ------- Substituting 1 for a, 8 for b, and 4 for c

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