document.write( "Question 1003803: Use the method of completing the square to find the standard form of the quadratic function.
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Algebra.Com's Answer #620440 by Edwin McCravy(20055)\"\" \"About 
You can put this solution on YOUR website!
Use the method of completing the square to find the standard form of the quadratic function.
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document.write( "We want to get it in the form\r\n" );
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document.write( "\"f%28x%29=a%28x-h%29%5E2%2Bk\"\r\n" );
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document.write( "where the vertex is (h,k) and the axis of symmetry\r\n" );
document.write( "is the vertical line whose equation is x=h.\r\n" );
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document.write( "Make sure it's in order of descending powers:\r\n" );
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document.write( "\"f%28x%29+=+x%5E2+%2B+6x+-+1\"\r\n" );
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document.write( "Factor out the coefficient of the first two terms.\r\n" );
document.write( "It's 1 here so this step isn't necessary, but I'll\r\n" );
document.write( "do it anyway so it'll be in the form \"f%28x%29=a%28x-h%29%5E2%2Bk\"\r\n" );
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document.write( "\"f%28x%29+=+1%28x%5E2+%2B+6x%29+-+1\"\r\n" );
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document.write( "1.  Multiply the coefficient of x, which is 6, by 1/2, getting 3.\r\n" );
document.write( "2.  Square the result of step 1, 32=9\r\n" );
document.write( "3.  Add and subtract that number, that is add + 9 - 9 after the 6x:\r\n" );
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document.write( "\"f%28x%29+=+1%28x%5E2+%2B+6x%2B9-9%29+-+1\"\r\n" );
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document.write( "Factor the first three terms:\r\n" );
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document.write( "\"f%28x%29+=+1%28%28x%2B3%29%28x%2B3%29%5E%22%22-9%29+-+1\"\r\n" );
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document.write( "If you followed the 3 steps above both factors are the same and\r\n" );
document.write( "it can be written as the square of a binomial:\r\n" );
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document.write( "\"f%28x%29+=+1%28%28x%2B3%29%5E2-9%29+-+1\"\r\n" );
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document.write( "Distribute to remove the outer (large) parentheses, leaving the\r\n" );
document.write( "square of the binomial intact:\r\n" );
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document.write( "\"f%28x%29+=+1%28x%2B3%29%5E2-9+-+1\"\r\n" );
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document.write( "Combine the remaining terms as -10\r\n" );
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document.write( "\"f%28x%29+=+1%28x%2B3%29%5E2-10\"\r\n" );
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document.write( "That's in the form \r\n" );
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document.write( "\"f%28x%29=a%28x-h%29%5E2%2Bk\"\r\n" );
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document.write( "where a=1, -h=+3, i.e., h=-3, k=-10\r\n" );
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document.write( "so the vertex is (h,k) = (-3,-10) and the axis of symmetry\r\n" );
document.write( "is the vertical line whose equation is x=h, or x=-3. \r\n" );
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document.write( "Edwin

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