I try to be positive. It's the only thing that turns it around. If they're toxic and bad and you're the one that's going to help the win the game then do it. Prove them wrong.
I recently had my mf cry a river about my sup trundle because she died when she all in'd at level 1 vs level 2's. Screamed how bad I was to go ward jg because I saw the enemy jg run that direction and i didn't want my jg to get killed and I pinged that I was doing it. I said sorry, don't stress it. We'll recover, I promise, we got this shit. Took her 5 levels to stop. At that point, I got an e (road block and slow) on their sup and got her a kill, ulted their adc and dived, yi peeled around the corner and took them out, I leave tower half health. I said gj guys, awesome gank. Let's clear their jg and dragon. And we did.
By the end of the game I was impossible for them to kill me or the mf and she was 10/5. I said encouraging things the whole time and they literally didn't say a thing the entire rest of the game.
Specifically, people want to vent and blame someone when they make a mistake... What I've found is to let them be frustrated, tell them you'll help them or make it up to them. Then do it. It's not foolproof. Sometime they're just going to go full retard and feed. But this has helped me turn things around a lot.