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Most of us grew up with parents who cared for us financially. So it can be jarring to begin to consider—or even take responsibility for—their fiscal well-being.

For most of us, it's hard to know if we'll ultimately need to pitch in; ill health and other surprises can derail even solid plans. A 2013 Merrill Lynch study found nearly two in five fiftysomethings had aided parents, with contributions totaling $15,000 on average.

For your own financial and emotional health, you should know where your parents stand and how you may need to help them. The first step is to sit down and—diplomatically—open the conversation. Here are a few questions to ask.

"Can we talk?" Don't just raise the subject randomly. Money topics are notoriously taboo. If your parents have kept you in the dark till now, they may not be eager to open up. Or they might be assuming you'll support them in the future, yet too nervous or embarrassed to admit it.

Set up the talk in advance, picking a time when you can be thoughtful and won't be rushed. If you have siblings, mention it to them first and include them. My own family had this discussion a few years ago. In our case, my brothers, both doctors, agreed to take responsibility for my mom's health care needs, while I helped her gather her financial accounts.

"Do you feel prepared?" If your parents are still working, ask about their retirement expectations. Be sure to express interest, not judgment—which could push them into a defensive stance.

Find out whether they've determined how much money they'll need and how they'll support themselves once they stop working. Suggest they experiment with an online retirement calculator; you can even help with the exercise, if they're willing. And ask about their plans for long-term care, should it become necessary.

Calculator: How much will I need to save for retirement?

"Where is your paperwork?" Your folks should have in place at least a will and documents naming people to make medical and financial decisions on their behalf, should they become unable to. Ask to digitize their paperwork. (I store my mom's files securely online.)

Suggest that your parents assemble a list of accounts and emergency contacts for their advisers, accountants, and lawyers. Getting organized is key. Depending on your relationship, your parents may even want to give you access to their accounts.

This won't be the easiest talk you've had, but it's essential—for both their financial security and your own peace of mind.

Columnist Alexa von Tobel is the founder of LearnVest.