document.write( "Question 921157: 4x^2+24x-13 converted into vertex form
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Algebra.Com's Answer #558764 by Edwin McCravy(20060)\"\" \"About 
You can put this solution on YOUR website!
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document.write( "Maybe the other tutor didn't break it down enough for you \r\n" );
document.write( "to understand.  Some people require a little more breakdown \r\n" );
document.write( "and explanation than others.  Here is the complete breakdown \r\n" );
document.write( "all the way to the graph.  Study it carefully and use it as\r\n" );
document.write( "a model for your other problems and you'll know how to do them\r\n" );
document.write( "all.\r\n" );
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document.write( "\"y+=+4x%5E2%2B24x-13\"\r\n" );
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document.write( "Factor 4 out of the first two terms. (Don't factor out 4x, just 4)\r\n" );
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document.write( "\"y+=+4%28x%5E2%2B6x%5B%22%22%5D%29-13\"\r\n" );
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document.write( "To the side:\r\n" );
document.write( "Multiply the coefficient of x, which is 6, by \"1%2F2\".  \"6%2Aexpr%281%2F2%29=3\"\r\n" );
document.write( "Square 3.   \"3%5E2=9\"\r\n" );
document.write( "Add +9-9 to the 6x inside the parentheses. (It doesn't affect the value\r\n" );
document.write( "because adding +9-9 is the same as adding 0.\r\n" );
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document.write( "\"y+=+4%28x%5E2%2B6x%2B9-9%5B%22%22%5D%29-13\"\r\n" );
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document.write( "To the side:\r\n" );
document.write( "Factor the first three terms inside the parentheses: x²+6x+9 = (x+3)(x+3)\r\n" );
document.write( "Write (x+3)(x+3) as (x+3)². \r\n" );
document.write( "Replace x²+6x+9 by (x+3)²\r\n" );
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document.write( "\"y+=+4%28%28x%2B3%29%5E2-9%5B%22%22%5D%29-13\"\r\n" );
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document.write( "Remve the BIG parentheses (not the small ones) by distributing the 4\r\n" );
document.write( "into the BIG parentheses leaving the small parentheses intact:\r\n" );
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document.write( "\"y+=+4%28x%2B3%29%5E2-36-13%29\"\r\n" );
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document.write( "Combine the -36-13 as -49\r\n" );
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document.write( "\"y+=+4%28x%2B3%29%5E2-49\"\r\n" );
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document.write( "That's it.  Compare it to\r\n" );
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document.write( "\"y+=+a%28x-h%29%5E2%2Bk%29\"\r\n" );
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document.write( "And see that -h = +3 which means h = -3\r\n" );
document.write( "             +k = -49 which means or k = -49\r\n" );
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document.write( "Which means the vertex point is (h,k) = (-3,-49)\r\n" );
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document.write( "and that the graph passes through the three points\r\n" );
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document.write( "1.  The vertex = (h,k) = (-3,-49)\r\n" );
document.write( "2.  The point just to the right of the vertex: (h+1,k+a) = (-3+1,-49+4) = (-2,-45)\r\n" );
document.write( "3.  The point just to the left of the vertex: (h-1,k+a) = (-3-1,-49+4) = (-4,-45)\r\n" );
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document.write( "Plot those three points and sketch the graph:\r\n" );
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document.write( "Edwin
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