How do I recover my website from Google penalty?

The best way to check if your website was penalized by an automatic penalty is to login to Google analytics and review your Google organic traffic. If you see a drop in traffic during the dates that Google released an algorithmic change, then most probably you were hit and that's the reason that your traffic dropped.

there are lot of ways to recover from penality , remove bad links, give some quality links and then resubmit site.

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