document.write( "Question 97832: what is the equation of the line of symmetry for y = -x² + 4x + 5 \n" ); document.write( "
Algebra.Com's Answer #71186 by Edwin McCravy(20056)\"\" \"About 
You can put this solution on YOUR website!
\r\n" );
document.write( "what is the equation of the line of symmetry for y = -x² + 4x + 5\r\n" );
document.write( "\r\n" );
document.write( "The vertex for the quadratic equation:\r\n" );
document.write( "\r\n" );
document.write( "y = ax² + bx + c\r\n" );
document.write( "\r\n" );
document.write( "is given by the formula:\r\n" );
document.write( "\r\n" );
document.write( "(\"-b%2F%282a%29\", \"-D%2F%284a%29\"), where D = discriminant = \"b%5E2-4ac\"\r\n" );
document.write( "\r\n" );
document.write( "and the line of symmetry is the vertical line\r\n" );
document.write( "whose equation is \r\n" );
document.write( "\r\n" );
document.write( "x = \"-b%2F%282a%29\"\r\n" );
document.write( "\r\n" );
document.write( "==============================\r\n" );
document.write( "\r\n" );
document.write( "For the quadratic equation:\r\n" );
document.write( "\r\n" );
document.write( "y = -x² + 4x + 5\r\n" );
document.write( "\r\n" );
document.write( "a = -1, b = 4, c = 5\r\n" );
document.write( "\r\n" );
document.write( "D = discriminant = \"b%5E2-4ac\" = \"4%5E2-4%2A-1%2A5\" = \"16%2B20\" = \"36\"\r\n" );
document.write( "\r\n" );
document.write( "So the vertex is\r\n" );
document.write( "\r\n" );
document.write( "(\"-b%2F%282a%29\", \"-D%2F%284a%29\") = (\"-4%2F%282%2A-1%29\", \"-36%2F%284%2A-1%29\") = \r\n" );
document.write( "(\"-4%2F%28-2%29\", \"-36%2F%28-4%29\") = (\"2\", \"9\"),    \r\n" );
document.write( "\r\n" );
document.write( "and the line of symmetry is the vertical line\r\n" );
document.write( "whose equation is \r\n" );
document.write( "\r\n" );
document.write( "x = \"-b%2F%282a%29\"\r\n" );
document.write( "\r\n" );
document.write( "or\r\n" );
document.write( "\r\n" );
document.write( "x = 2\r\n" );
document.write( "\r\n" );
document.write( "Here is the graph of the quadratic and the\r\n" );
document.write( "green vertical line is the line of symmetry,\r\n" );
document.write( "notice it crosses the x axis at 2.\r\n" );
document.write( "\r\n" );
document.write( "\"graph%28222.2222222%2C375%2C-3%2C7%2C-8%2C10%2C+-x%5E2%2B4x%2B5%2C999%28x-2%29%29\"\r\n" );
document.write( "\r\n" );
document.write( "Edwin
\n" ); document.write( "
\n" );