document.write( "Question 197245: Hello, I have to provide a real life example of quadratic function. I have no idea where to start. Can you help me with some ideas and formulas for the everyday use of quadratic function? Thank you. \n" ); document.write( "
Algebra.Com's Answer #147879 by Edwin McCravy(20056)\"\" \"About 
You can put this solution on YOUR website!
\r\n" );
document.write( "A rectangular field adjacent to the straight bank of a river is to \r\n" );
document.write( "be fenced, but there is to be no fencing along the riverbank. If 180 m \r\n" );
document.write( "of fencing is available, what is the maximum area that can be \r\n" );
document.write( "enclosed?\r\n" );
document.write( "\r\n" );
document.write( "We draw a rectangle for the area, with a dotted line\r\n" );
document.write( "for the river bank:\r\n" );
document.write( "\r\n" );
document.write( " \r\n" );
document.write( "\r\n" );
document.write( "If we let x ft. be the length of the left and right sides,\r\n" );
document.write( "the bottom side will be 200 ft - 2x ft.  So we put x on\r\n" );
document.write( "the two vertical sides and 200-2x on the horizontal side.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "Let y = the area of the rectangle.\r\n" );
document.write( "\r\n" );
document.write( "Use \"Area+=+%28base%29%28height%29\", so we have\r\n" );
document.write( "\r\n" );
document.write( "\"y=%28200-2x%29%28x%29\"\r\n" );
document.write( "\r\n" );
document.write( "\"y=x%28200-2x%29\"\r\n" );
document.write( "\r\n" );
document.write( "\"y=200x-2x%5E2\"\r\n" );
document.write( "\r\n" );
document.write( "\"y=-2x%5E2%2B200x\"  (Note: this is a quadratic equation)\r\n" );
document.write( "\r\n" );
document.write( "If we draw the graph of that we get:\r\n" );
document.write( "\r\n" );
document.write( "\"graph%28400%2C400%2C-10%2C105%2C-200%2C5100%2C200x-2x%5E2%29\"\r\n" );
document.write( "   \r\n" );
document.write( "Since the graph is symmetrical, the highest point\r\n" );
document.write( "is right in the middle between the two x-intercepts.\r\n" );
document.write( "\r\n" );
document.write( "So we find the two x-intercepts by setting y=0 and\r\n" );
document.write( "solving for x:\r\n" );
document.write( "\r\n" );
document.write( "\"y=-2x%5E2%2B200x\"\r\n" );
document.write( "\"0=-2x%5E2%2B200x\"\r\n" );
document.write( "\"2x%5E2-200x=0\"\r\n" );
document.write( "\r\n" );
document.write( "Factor the left side:\r\n" );
document.write( "\r\n" );
document.write( "\"2x%28x-100%29=0\"\r\n" );
document.write( "\r\n" );
document.write( "\"2x=0\",  \"x-100=0\"\r\n" );
document.write( "\"x=0\",   \"x=100\"\r\n" );
document.write( "\r\n" );
document.write( "Halfway between those will be\r\n" );
document.write( "where x = 50\r\n" );
document.write( "\r\n" );
document.write( "So the two vertical sides will be 50 feet each,\r\n" );
document.write( "and the base will be 200 - 2x or\r\n" );
document.write( "\r\n" );
document.write( "\"200-2x=200-2%2850%29=200-100=100\"\r\n" );
document.write( "\r\n" );
document.write( "or 100 feet.  And that maximum area will be\r\n" );
document.write( "\r\n" );
document.write( "(base)(height) = (100)(50) = 5000 square feet.\r\n" );
document.write( "\r\n" );
document.write( "Edwin
\n" ); document.write( "
\n" );