Can I claim a 17 year old dependent if the worked and made over 10000? Or do they need to file there own taxes?

It depends. If the person you are trying to claim meets the qualifying requirements of a qualifying child it doesn't matter how much they made, but they may have to file their own tax return if they meet the filing requirements.  Have your dependent review the IRS website: Check if you need to file a tax return to determine if they are required to file a tax return. They also should file a tax return to get a refund of their federal and/or state withholdings. 

To determine if the individual is your qualifying child, the following questions must be true:

• The child must be related to you. 
• The child can’t be claimed as a dependent by someone else. 
• The child must be a U.S. citizen, resident alien, national, or a Canadian or Mexican resident. 
• If the child is married, they can’t file a joint return with their spouse. 
• The child must be under the age of 19 (or 24 for full-time students). 
  • No age limit for permanently and totally disabled children. 
• The child must have lived with you for more than half the year (exceptions apply). 
• The child didn't provide more than half of their own support for the year. 

If your dependent files their own tax return, make sure that they indicate that someone else is claiming them as a dependent.  Refer to the TurboTax article: How do I indicate that I can be claimed as a dependent on someone else's return.

But ...yes, they do need to file their own tax return....their working income cannot go on your tax return.

And, as @SharonD007  noted, when preparing theirs, it needs to indicate that someone else (i.e. you) will be claiming them as a dependent.

 Don't let them do it alone, work on it together.....and IF using the Online software, don't try to use your account to prepare and file it.  If using Online software, you'll have to create a new UserID/pwd for the dependent's tax return.