I think japanworm do not want it on the frontpage, the code above let’s it display only on the frontpage.
You can exclude something (if not) by putting an ! before the tag.
What you want to say is:
If it isn’t front page than display the form
So it would actually be
<?php if( !is_front_page() ) { //if we are not on the front page ?>
the code of your form
<?php } ?>