document.write( "Question 284560: it says use complete the square to transform the equation to graphing form then graph it\r
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Algebra.Com's Answer #206453 by Edwin McCravy(20060)\"\" \"About 
You can put this solution on YOUR website!

\n" ); document.write( "it says use complete the square to transform the equation to graphing form then graph it\r
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document.write( "This is the equation of a circle because it has \r\n" );
document.write( "both an \"x%5E2\" and a \"y%5E2\" term which have\r\n" );
document.write( "the same coefficients when on the same side of the\r\n" );
document.write( "equation.\r\n" );
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document.write( "We want to get it looking like this standard form\r\n" );
document.write( "for a circle's equation:\r\n" );
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document.write( "\"%28x-h%29%5E2%2B%28y-k%29%5E2=r%5E2\"\r\n" );
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document.write( "where the center is (h,k) and the radius is r\r\n" );
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document.write( "\"3x%5E2%2B3y%5E2-12x-24y%2B12=0\"\r\n" );
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document.write( "Divide through by 3\r\n" );
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document.write( "\"x%5E2%2By%5E2-4x-8y%2B4=0\"\r\n" );
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document.write( "Swap the two middle terms to get the x-term next to\r\n" );
document.write( "the \"x%5E2\"-term and the \"y%5E2\"-term next to the\r\n" );
document.write( "y-term. Also add 4 to both sides:\r\n" );
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document.write( "\"+x%5E2-4x%2By%5E2-8y=-4+\"\r\n" );
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document.write( "Complete the square on the first two terms:\r\n" );
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document.write( "1. Multiply the coefficient of x, which is -4, by \"1%2F2\"\r\n" );
document.write( "   getting -2\r\n" );
document.write( "2. Square -2, getting \"%28-2%29%5E2\" or \"%22%22%2Bred%284%29\".\r\n" );
document.write( "3. Add \"%22%22%2Bred%284%29\" to both sides:\r\n" );
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document.write( "\"x%5E2-4x%2Bred%284%29%2By%5E2-8y=-4%2Bred%284%29\"\r\n" );
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document.write( "Complete the square on the last two terms on the left:\r\n" );
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document.write( "1. Multiply the coefficient of y, which is -8, by \"1%2F2\"\r\n" );
document.write( "   getting -4\r\n" );
document.write( "2. Square -4, getting \"%28-4%29%5E2\" or \"%2Bgreen%2816%29\".\r\n" );
document.write( "3. Add \"%22%22%2Bgreen%2816%29\" to both sides:\r\n" );
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document.write( "\"x%5E2-4x%2Bred%284%29%2By%5E2-8y%2Bgreen%2816%29=-4%2Bred%284%29%2Bgreen%2816%29\"\r\n" );
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document.write( "1. Factor the trinomial consisting of the first three terms on the left.\r\n" );
document.write( "2. Factor the trinomial consisting of the last three terms on the left.\r\n" );
document.write( "3. Combine the numbers on the right.\r\n" );
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document.write( "\"+%28x-2%29%5E2+%2B+%28y-4%29%5E2+=+16+++\"\r\n" );
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document.write( "Write the \"16\" as \"4%5E2\"\r\n" );
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document.write( "Compare to\r\n" );
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document.write( "\"%28x-h%29%5E2%2B%28y-k%29%5E2=r%5E2\"\r\n" );
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document.write( "and the center is (h,k) = (2,4) and the radius is r=4\r\n" );
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document.write( "The graph is drawn with a compass, since it is a circle.\r\n" );
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document.write( "Put the sharp point of the compass at the center (2,3):\r\n" );
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document.write( " Open the compass to 4 units, and draw this circle:\r\n" );
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document.write( "Edwin

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