document.write( "Question 1164308: The parabolic graph of the function f(x) = ax^2 + bx + c passes through the points with
\n" ); document.write( "coordinates (1, 4), (2, 8), and (3, 14). Find a matrix equation for the coefficients a, b, and c. \n" ); document.write( "
Algebra.Com's Answer #788646 by ikleyn(52803)\"\" \"About 
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document.write( "To get your first equation, substitute x= 1 into the formula (first point (1,4)).\r\n" );
document.write( "You will get then\r\n" );
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document.write( "    f(1) = a*1^2 + b*1 + c = 4,   or\r\n" );
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document.write( "           a     + b   + c = 4.     (1)\r\n" );
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document.write( "To get your second equation, substitute x= 2 into the formula (second point (2,8)).\r\n" );
document.write( "You will get then\r\n" );
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document.write( "    f(2) = a*2^2 + b*2 + c = 8,   or\r\n" );
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document.write( "           4a    + 2b  + c = 8.     (2)\r\n" );
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document.write( "To get your third equation, substitute x= 3 into the formula (third point (3,14)).\r\n" );
document.write( "You will get then\r\n" );
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document.write( "    f(3) = a*3^2 + b*3 + c = 14,   or\r\n" );
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document.write( "           9a    + 3b  + c = 14.     (3)\r\n" );
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document.write( "In matrix form, your equation now is\r\n" );
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document.write( "           \"%28matrix%283%2C3%2C+1%2C1%2C1%2C++4%2C2%2C1%2C++9%2C3%2C1%29%29\".\"%28matrix%283%2C1%2C+a%2Cb%2Cc%29%29\" = \"%28matrix%283%2C1%2C+2%2C8%2C14%29%29\".     (4)\r\n" );
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document.write( "You should see the coefficients of the equations (1), (2) and (3) as the first, second and third rows \r\n" );
document.write( "of the coefficient matrix, respectively.\r\n" );
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document.write( "You also should see the right side terms of the equations (1,), (2) and (3) in the right side vector (4).\r\n" );
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