How do I turn off notifications from the home screen of my iPhone in iOS 9?
Those are not notifications, those are apps that are suggested by iOS due to location and usage, or by Handoff from your other devices.

To change the settings for those, change the toggles in General &gt; Handoff &amp; Suggested Apps in the Settings app. Toggle everything off if you do not use Handoff and do not want to see any suggestions.