Why can't I display "Search result" in the search results?

This may seem an odd question, but here is what I am trying to do. I have switched on Search (core Search that is) on a little test site, and it works. I have also switched on DS and modified the display of one of my content types, and that works.
What I would now like to do is to modify the search display so that it displays the attached image, plus the returned results from the Search (ie the same that comes back from the ordinary core Search). But I cannot see this option anywhere, which seems a bit odd. It seems the only thing I can do is to create a display for search results using the image and the teaser for example.