document.write( "Question 1198846: 5. Convert the following equation into vertex form by completing the square.
\n" ); document.write( "f(x) = 2x^2+12x-4
\n" ); document.write( "

Algebra.Com's Answer #832500 by Edwin McCravy(20056)\"\" \"About 
You can put this solution on YOUR website!
\r\n" );
document.write( "The vertex form of a parabola is:\r\n" );
document.write( "\r\n" );
document.write( "\"%22f%28x%29%22=+a%28x-h%29%5E2%2Bk\" where (h,k) is the vertex.\r\n" );
document.write( "\r\n" );
document.write( "\"%22f%28x%29%22+=+2x%5E2%2B12x-4\"\r\n" );
document.write( "\r\n" );
document.write( "Factor 2 out of the first two terms only:\r\n" );
document.write( "\r\n" );
document.write( "\"%22f%28x%29%22+=+2%28x%5E2%2B6x%29-4\"\r\n" );
document.write( "\r\n" );
document.write( "We must add and subtract the proper number inside the parentheses to\r\n" );
document.write( "cause \"x%5E2%2B6x\" to become a perfect square.  To do that we take\r\n" );
document.write( "1/2 of the coefficient of x, which is 6.  1/2 of 6 is 3.  Then we\r\n" );
document.write( "square 3 and get 9.  So 9 is the number we must add, then subtract,\r\n" );
document.write( "i.e., +9-9 inside the parentheses:\r\n" );
document.write( "\r\n" );
document.write( "\"%22f%28x%29%22+=+2%28x%5E2%2B6x%2B9-9%29-4\"\r\n" );
document.write( "\r\n" );
document.write( "Next we factor only the first three terms inside the parentheses:\r\n" );
document.write( "\r\n" );
document.write( "\"%22f%28x%29%22+=+2%28%28x%2B3%29%28x%2B3%29%5E%22%22-9%29-4\"\r\n" );
document.write( "\r\n" );
document.write( "And, as you see it factors as the square of a binomial:\r\n" );
document.write( "\r\n" );
document.write( "\"%22f%28x%29%22+=+2%28%28x%2B3%29%5E2-9%29-4\"\r\n" );
document.write( "\r\n" );
document.write( "Next we distribute the 2 into the parentheses leaving the (x+3)2 intact.\r\n" );
document.write( "\r\n" );
document.write( "\"%22f%28x%29%22+=+2%28x%2B3%29%5E2-18-4\"\r\n" );
document.write( "\r\n" );
document.write( "\"%22f%28x%29%22+=+2%28x%2B3%29%5E2-22\"\r\n" );
document.write( "\r\n" );
document.write( "Comparing to \r\n" );
document.write( "\r\n" );
document.write( "\"%22f%28x%29%22=+a%28x-h%29%5E2%2Bk\" where (h,k) is the vertex.\r\n" );
document.write( "\r\n" );
document.write( "The vertex is (h,k) = (-3,-22)\r\n" );
document.write( "\r\n" );
document.write( "Edwin
\n" ); document.write( "
\n" );