document.write( "Question 778461: Write the function in vertex form.
\n" ); document.write( "y=x^2-3x+6 \n" ); document.write( "

Algebra.Com's Answer #474653 by Edwin McCravy(20055) $\"\"$ $\"About$

You can put this solution on YOUR website!

\r\n" );
document.write( "We want to get y = a(x-h)²+k \r\n" );
document.write( "\r\n" );
document.write( "y = x²-3x+6 in the form \r\n" );
document.write( "\r\n" );
document.write( "Put brackets around the first two terms on the\r\n" );
document.write( "right,\r\n" );
document.write( "\r\n" );
document.write( "y = [x²-3x]+6\r\n" );
document.write( "\r\n" );
document.write( " and since the coefficient of x² is 1 put 1\r\n" );
document.write( "in front of the parentheses. Normally you\r\n" );
document.write( "would factor out the coefficient of x²:\r\n" );
document.write( "\r\n" );
document.write( "y = 1[x²-3x]+6\r\n" );
document.write( "\r\n" );
document.write( "We complete the square inside the brackets:\r\n" );
document.write( "\r\n" );
document.write( "1. Multiply the coefficient of x, which is -3\r\n" );
document.write( "   by , getting .\r\n" );
document.write( "2. Square  getting  = \r\n" );
document.write( "3. Add , which is really 0, inside the\r\n" );
document.write( "   brackets:\r\n" );
document.write( "\r\n" );
document.write( "y = 1[x²-3x+-]+6\r\n" );
document.write( "\r\n" );
document.write( "Factor the first three terms inside the bracket like this\r\n" );
document.write( "             x²-3x+ = (x-)(x-) = (x-)²\r\n" );
document.write( "\r\n" );
document.write( "y = 1[(x-)²-]+6\r\n" );
document.write( "\r\n" );
document.write( "Remove the bracket\r\n" );
document.write( "\r\n" );
document.write( "y = 1(x-)²-+6 \r\n" );
document.write( "\r\n" );
document.write( "Write the 6 as \r\n" );
document.write( "\r\n" );
document.write( "y = 1(x-)²-+\r\n" );
document.write( "\r\n" );
document.write( "y = 1(x-)²+ \r\n" );
document.write( "\r\n" );
document.write( "y = a(x-h)²+k\r\n" );
document.write( "\r\n" );
document.write( "The vertex is (h,k) = (,)\r\n" );
document.write( "\r\n" );
document.write( "Edwin

\n" ); document.write( "

\n" );