When you’re putting on a local event, a full-featured approach is to have both hard-copy flyers to post in the physical community AND online graphics that you can use for the Facebook Event, ads, and other web promotions.
For Katherine’s series of local workshops, we crafted a paper flyer (and PDF version) that was attractive and clearly laid out an impressive amount of information. Then we created other graphics specifically for online promotions. This is almost always a better idea than just chopping and resizing your one graphic for use in all places. Various online venues have different size and proportion requirements, and many overlay text or other elements onto your image, so it’s best to design specifically for them.