what do you do when your parents find out about your search history?

Your folks are just keeping you safe.  That's their job.  If they're upset, just apologize and do as you're told.  It really is for your own good.  

Own up to it, if you weren't clever enough to delete it prior to their finding out. If you're old enough to be doing internet searches, you're old enough to take responsibility for them. 

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Your question belongs in Family & Relationships>Family as it's currently in Yahoo Products>Yahoo Search and not actually applicable to this subcategory (and thus decreases your chances of getting many useful answers).

Moving your question can be done by clicking Edit (pencil icon for mobile)>Edit category just beneath your question, then selecting the category that's appropriate for the topic.

Say you lent it to a friend..

What do I do when my parents find out about my search history?

Marvel.

I'm 70 and they've been dead a long, long time.

It's high time you learned about private browsing, when your internet browser opens a new window that does not save cookies or history. In a private window, no one but you will know what your search terms were.

If you think your parents don't know about all the weird stuff you're watching, think again. Look into how routers work, look into how your HDD works, look into how your temp storage works. You could delete every single trace of your browsing history, but its impossible to get rid of it for good. X'D