document.write( "Question 976598: What is the formula and checking if this in quadratic form of 1,3,17,31,49.... \n" ); document.write( "
Algebra.Com's Answer #598165 by Edwin McCravy(20056)\"\" \"About 
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document.write( "A quadratic is of degree 2.  If the 2nd differences are all the\r\n" );
document.write( "same then it is quadratic form.   \r\n" );
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document.write( "Write the first and second differences by\r\n" );
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document.write( "To get the first differences:\r\n" );
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document.write( "1. List the numbers in a column\r\n" );
document.write( "2. For each number in the column, subtract it from the number just\r\n" );
document.write( "   below it and write it to the right of that number.  \r\n" );
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document.write( "To get the second derivative, do the same with the column of first \r\n" );
document.write( "differences\r\n" );
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document.write( " 1  2  12\r\n" );
document.write( " 3 14 -10\r\n" );
document.write( "17  4  24\r\n" );
document.write( "21 28\r\n" );
document.write( "49\r\n" );
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document.write( "The second differences are not all the same, so it is not a quadratic form.\r\n" );
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document.write( "Here is another set of values that ARE in quadratic form for your comparison:\r\n" );
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document.write( "If the numbers were 1, 6, 15, 28, 45, we would make the first and second differences:\r\n" );
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document.write( " 1  5  4\r\n" );
document.write( " 6  9  4\r\n" );
document.write( "15 13  4\r\n" );
document.write( "28 17 \r\n" );
document.write( "45\r\n" );
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document.write( "And in this case the second differences are all the same, 4, so it is in\r\n" );
document.write( "quadratic form.\r\n" );
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document.write( "Then we would substitute in (1,1), (2,6), (3,15) in\r\n" );
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document.write( "y = Ax²+Bx+C\r\n" );
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document.write( "Get three equations in A, B, and C and solve for A, B and C, getting\r\n" );
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document.write( "A=2, B=-1, C=0  and the equation \r\n" );
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document.write( "y = Ax²+Bx+C\r\n" );
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document.write( "would become\r\n" );
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document.write( "y = 2x²-x\r\n" );
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document.write( "Edwin

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