document.write( "Question 237370: write an equation in standard form of the parabola that has the same shape as the graph of $\"f%28x%29=-7x%5E2\"$ , but which has a maximum of $\"9\"$ at $\"x=3\"$ . \n" ); document.write( "

Algebra.Com's Answer #174565 by Edwin McCravy(20056) $\"\"$ $\"About$

You can put this solution on YOUR website!

\r\n" );
document.write( "First let's draw the graph of the first equation:\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "Notice that since its vertex is  it has a maximum\r\n" );
document.write( "of  at .  Now let's plot the point .\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "We now need to shift the graph of  so that its\r\n" );
document.write( "vertex  shifts to the point  and the second shifted function .\r\n" );
document.write( "\r\n" );
document.write( "We first shift the graph horizontally 3 units to the right.\r\n" );
document.write( "This is done by replacing  in the right side of  by \r\n" );
document.write( ", getting . \r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "But now that graph must be shifted vertically upward by  units.\r\n" );
document.write( "This is done by adding  to the right side of ,\r\n" );
document.write( "getting .  Now we draw that graph, and get\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "So the answer is }.  Notice that it has the\r\n" );
document.write( "same shape as the original graph of .\r\n" );
document.write( "\r\n" );
document.write( "Edwin

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

\n" );