I have a 17 year old daughter do I need to pay child support if she goes to college and turns 18? I live in California.

It will be up to the child support agreement you have in place. Normally yes, you will, and often pay for part of the college expenses also

Unless your court papers say different then no. You won't have to pay child support after 18 or until completion of high school and 19. If you have a rrears then it can go on for forever but as far as child support it stops at 18 ( age of emancipation ) so long as they have completed high school.
California Courts: Self-Help Center (http://www.courtinfo.ca.gov/selfhelp/)
You might find that handy for future reference.