document.write( "Question 90260This question is from textbook
\n" ); document.write( ": Find the maximum value of y=x squared+6x \n" ); document.write( "
Algebra.Com's Answer #65542 by jim_thompson5910(35256)\"\" \"About 
You can put this solution on YOUR website!
Are you sure it's not the minimum? No maximum occurs on the graph of \"y=x%5E2%2B6x\". Well here's the solution to find the minimum\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "The minimum value occurs at the vertex of the graph\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "First determine the x-value of the vertex:\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "\"x=-b%2F%282a%29\" Here is the general formula to find the x-value of the vertex\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "From the equation \"y=x%5E2%2B6x\" we can see that a=1 and b=6\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "\"x=%28-6%29%2F%282%2A1%29\" Plug in b=6 and a=1\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "\"x=%28-6%29%2F2\" Multiply 2 and 1 to get 2\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "\"x=-3\" Reduce\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "So the x-coordinate of the vertex is \"x=-3\". Lets plug this into the equation to find the y-coordinate of the vertex.\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "Lets evaluate \"f%28-3%29\"\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "\"f%28x%29=x%5E2%2B6x\" Start with the given polynomial\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "\"f%28-3%29=%28-3%29%5E2%2B6%28-3%29\" Plug in \"x=-3\"\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "\"f%28-3%29=%289%29%2B6%28-3%29\" Raise -3 to the second power to get 9\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "\"f%28-3%29=%289%29%2B-18\" Multiply 6 by -3 to get -18\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "\"f%28-3%29=-9\" Now combine like terms\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "So the vertex is (-3,-9)\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "So the minimum value is -9\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "If we graph \"y=x%5E2%2B6x\", we can clearly see the minimum value\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "
\n" );