Don't assume that your daughter has faulty thinking just because she does not open up. She may be closed off because she does not know what to say about some confusing situation around her, or because of some previous traumatic experience, or because something else we do not even consider. She may even be quiet because she feels alone in subscribing to the wholesome anchor thoughts she has. I don't have all the information I need to make a judgment. Anyway, you can't go wrong by probing gently or getting professional help to assist her in expressing herself.
Without her words, you still have her attitude and actions to discern. Based on these, ask her help: "Please help me understand what you think about (something that's happening, something someone said, something she herself)?" "I'd really like to know if you're pleased or displeased with . . ." Also, if she is a teen, get some tips from another of my articles titled, "Why Is It So Difficult to Get Through to Teens?"
The start is improved communication and trust between both of you, or you would not really know what misconceptions she holds, let alone how to replace them. Meanwhile, remain daughter friendly, touch her, hug her (if she'd let you), let her feel, see and hear your love. "Love is patient" and "Love never fails." (1 Corinthians 13: 4, 7) If you're a believer, let her hear you praying for her.