document.write( "Question 1003347: f(x) = −x^2 + 8x + 3\r
\n" ); document.write( "\n" ); document.write( "find the maximum value of the function \n" ); document.write( "

Algebra.Com's Answer #620072 by MathLover1(20850) $\"\"$ $\"About$

You can put this solution on YOUR website!
$\"f%28x%29+=+-x%5E2+%2B+8x+%2B+3\"$ \r
\n" ); document.write( "\n" ); document.write( "the maximum value of the function will be $\"y\"$ coordinate of vertex; so, write equation in vertex form $\"f%28x%29+=+a%28x-h%29%5E2+%2B+k\"$ \r
\n" ); document.write( "\n" ); document.write( " $\"f%28x%29+=+-%28x%5E2+-8x%29+%2B+3\"$ ...........complete square\r
\n" ); document.write( "\n" ); document.write( " $\"f%28x%29+=+-1%2A%28x%5E2+-8x%2Bb%5E2%29-%28-1%29b%5E2+%2B+3\"$ \r
\n" ); document.write( "\n" ); document.write( " $\"f%28x%29+=+-%28x%5E2+-8x%2B4%5E2%29%2B1%2A4%5E2+%2B+3\"$ \r
\n" ); document.write( "\n" ); document.write( " $\"f%28x%29+=+-%28x+-4%29%5E2%2B16+%2B+3\"$ \r
\n" ); document.write( "\n" ); document.write( " $\"f%28x%29+=+-%28x+-4%29%5E2%2B19\"$ \r
\n" ); document.write( "\n" ); document.write( "so, $\"h=4\"$ and $\"k=19\"$ ,vertex is at ( $\"4\"$ , $\"19\"$ )\r
\n" ); document.write( "\n" ); document.write( "=>the maximum value of the function will be $\"y=19\"$ \r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "

\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( " \n" ); document.write( "

\n" );