Honestly, and it took me a while to see this myself, but EVERY question about lens/mirrors can be answered with the equation: 1/f = 1/do + 1/di; m = -di/do, and P = 1/f seriously EVERY single question.
Try plugging in an object distance for the concave (converging mirror) and then shortening the object distance. Make up some arbitrary focal length, and see what happens when the object is at 2f, at 1f, at 1/2f, at 1/5f, etc.
This will truly explain, in mathematical terms, why when you are at the focal length there is no image, because then 0 = 1/di and di = infinity. Play with this equation and the magnification equation and you will literally be able to understand perfectly why and when an image will be virtual, real, enlarged, shrunk, no image, etc.