You asked

What's the best way to initiate a conversation about sex with my child?

Firstly, parents should realise that they won’t be able to plan these conversations as conversations with teenagers rarely take place when and how their parents want them to. If you’re the one who initiates the conversation about sex, don’t be offended if your child looks appalled that you have done so. The important thing is that she knows that you are willing to discuss it.
Your teenager both does and does not want to discuss sex with you. Try to stay open to the topic whenever your child brings it up, she may bring the topic up when you least expect it. Lots of parents find that these topics often take place in cars, which have the advantage of being in private spaces in which you don’t have to look at one another.
Another useful approach may be to buy a good readable book for teenagers on sexual development. Before buying it, flick through to make sure you like its approach. Leave the book in her room where she can read it in private and let her know casually that you left it there and tell her if she wants to read it she can. This may help her feel that she can open up to you about the subject.

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