Wikipedia's front page can't be edited.
Can such a front page also be made with MediaWiki, so the users can't edit it?
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Yes, you need to protect it so that it can only be edited by administrators:
You can designate a page as a protected page by clicking the 'Protect page' tab ('protect' in the drop-down menu in Vector), and supplying a comment (a brief textual description of why you are protecting the page).
You will need to configure your IIS/Apache/WebServer so that it points to an index file that is completely separate from MediaWiki. Throw in a text input and submit button for the search and have it post to MediaWiki's search. This way, you've got a static home page that users cannot edit with a functional search.