document.write( "Question 898531: Put Into Vertex Form:
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Algebra.Com's Answer #544881 by Edwin McCravy(20060)\"\" \"About 
You can put this solution on YOUR website!
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document.write( "I'll just do the second one.  You do the others the same way:\r\n" );
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document.write( "\"y\"\"%22%22=%22%22\"\"3x%5E2-4x%2B5\"\r\n" );
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document.write( "Factor 3 out of the first two terms only.  Since 4 is not \r\n" );
document.write( "divisible by 3 and we have to take out a 3 anyway, we must \r\n" );
document.write( "divide the 4 by 3 and get a fraction. \r\n" );
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document.write( "\"y\"\"%22%22=%22%22\"\"3%28x%5E2-expr%284%2F3%29x%29%2B5\"\r\n" );
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document.write( "Next we complete the square inside the parentheses:\r\n" );
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document.write( "1. Multiply the coefficient of the term in x, which is \"-4%2F3\",\r\n" );
document.write( "   by \"1%2F2\", getting \"expr%28-4%2F3%29%2Aexpr%281%2F2%29=-4%2F6=-2%2F3\"\r\n" );
document.write( "2. Square this \"%28-2%2F3%29%5E2=4%2F9\"\r\n" );
document.write( "3. Add and subtract \"4%2F9\" inside the parentheses:\r\n" );
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document.write( "\"y\"\"%22%22=%22%22\"\"3%28x%5B%22%22%5D%5E2-expr%284%2F3%29x%2B4%2F9-4%2F9%29%2B5\"\r\n" );
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document.write( "Group the first three terms in smaller parentheses inside the\r\n" );
document.write( "larger parentheses:\r\n" );
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document.write( "\"y\"\"%22%22=%22%22\"\"3%28%28x%5E2-expr%284%2F3%29x%2B4%2F9%29-expr%284%2F9%29%5B%22%22%5D%29%2B5\"\r\n" );
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document.write( "The inner parentheses trinomial factors like this:\"x%5E2-expr%284%2F3%29x%2B4%2F9=%28x-2%2F3%29%28x-2%2F3%29=%28x-2%2F3%29%5E2\"\r\n" );
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document.write( "\"y\"\"%22%22=%22%22\"\"3%28%28x-2%2F3%29%5E2%5B%22%22%5D-4%2F9%29%2B5\"\r\n" );
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document.write( "Now we distribute to remove the large parentheses, leaving the smaller\r\n" );
document.write( "parentheses intact:\r\n" );
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document.write( "\"y\"\"%22%22=%22%22\"\"3%28x-2%2F3%29%5E2-3%2Aexpr%284%2F9%29%2B5\"\r\n" );
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document.write( "Then we complete the fraction work on the end.\r\n" );
document.write( "Cancel the 3 into the 9 and we have\r\n" );
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document.write( "\"y\"\"%22%22=%22%22\"\"3%28x-2%2F3%29%5E2-4%2F3%2B5\"\r\n" );
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document.write( "Get a common denominator of 3 by multiplying the 5 by \"3%2F3\"\r\n" );
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document.write( "\"y\"\"%22%22=%22%22\"\"3%28x-2%2F3%29%5E2-4%2F3%2B15%2F3\"\r\n" );
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document.write( "And the final vertex form is:\r\n" );
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document.write( "\"y\"\"%22%22=%22%22\"\"3%28x-2%2F3%29%5E2%2B11%2F3\"\r\n" );
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document.write( "Edwin
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