Do you need to do this before or after you query the user? That is, do you want to query only users who have mediaProfiles?
If so, you can do this:
User::has('mediaProfile')->get();
If you need to be more specific:
User::whereHas('mediaProfile', function($q) {
$q->where('some_status', 'whatever'); // in this scope, `$q` refers to the MediaProfile object, not the User.
});
If you need to check whether the user has a media profile after you've already gotten the user, you should simply be able to do:
if (is_null($user->mediaProfile)) { ... }
Since a relation returns null if it can't be found.