https://support.apple.com/en-us/HT201330
That’s it, that’s the only time you need to do it.
"Generally, there's no need to force an app to close unless it's unresponsive. When you press the Home button two times quickly, the recently used apps that appear aren't open. They're in an efficient standby mode to help you navigate and multitask.”
...
Some apps will run for a short period of time before they're set to a suspended state. This means they're not actively in use, open, or taking up system resources. When you return to these apps, they'll open instantly.
https://support.apple.com/en-us/HT202070
The simplistic nature of swiping apps off of the multitasking landing pad, and subsequently "quitting" them, helped create a widespread belief that an iPhone's battery could be preserved for a little longer. But as many have pointed out over the years, doing so could in fact do the complete opposite: you could be shortening the battery life of your iPhone.
http://www.macrumors.com/2016/03/10/force-quitting-apps-doesnt-help-battery/
And if you don’t want to take Apples word for it…
"don't force close your apps. Unless they are having a problem that is. If the app isn't responding, is crashing, etc., force close. If, on the other hand, it's working great, do not close those apps. By force closing all of your apps you are negatively impacting both battery life and performance of the device."
http://www.reddit.com/r/apple/comments/2h0hqq/psa_dont_force_close_your_apps/
"for most apps, you never -- not ever -- need to "delete" them or close them from the multitasking dock. You might feel a desire to, even an obsession to. But you really don't need to. Really.”
"You don't ever -- never as in not ever -- have to close ALL the apps in your multitasking, fast app switcher dock. It's a sniper rifle, not a nuke. So just relax and enjoy your apps and let iOS do the heavy lifting for you."
http://www.imore.com/tipb-answers-close-apps-multitasking-dock
"It's long been prescribed that when your iPhone's battery is running poorly that you close out all the running apps to help preserve battery life (we've mentioned it before). That makes sense if you're using a computer, but as writer (and former Genius Bar technician) Scotty Loveless points out, that's simply not the case in iOS.:
http://lifehacker.com/quitting-apps-in-ios-actually-worsens-battery-life-1560086834
"Despite what you may have heard, closing apps on your iPhone or iPad won’t speed it up. But iOS does allow apps to run in the background sometimes, and you can manage that in a different way.
This myth is actually harmful. Not only will it slow down your use of your device, but it could use more battery power in the long run. Just leave those recent apps alone!”
"Believe it or not, removing apps from memory using the multitasking interface could actually lead to less battery life in the long run. When you re-open such an app, your phone will have to read its data into RAM from your device’s storage and re-launch the app. This takes longer and uses more power than if you had just let the app suspend peacefully in the background."
"We've heard some folks say that you should close every application from the multitasking tray after you're done using it. That's simply not required."
http://www.techrepublic.com/article/understanding-multitasking-on-ios-should-you-quit-apps/