The Edit quiz settings quiz report
http://moodle.org/plugins/quiz_editquizsettings

This 'report' is actually a tool which lets users edit certain settings, currently
the open and close dates, for a quiz, without needing to give them permission to
edit all the other quiz settings.

This version of the plugin, which is compatible with Moodle 3.4+ and later.
Older versions of this plugin will work with older Moodle versions.

You can install it from the Moodle plugins database using the link above.

Alternatively, you can install it using git. In the top-level folder of your
Moodle install, type the command:
    git clone git://github.com/moodleou/moodle-quiz_editquizsettings.git mod/quiz/report/editquizsettings
    echo '/mod/quiz/report/editquizsettings/' >> .git/info/exclude

Then visit the admin screen to allow the install to complete.

Once the plugin is installed, you can access the functionality by going to
Reports -> Edit quiz settings in the Quiz administration block.