She managed to ______ her fears during the presentation.

Keep at bay means to prevent something from coming too close or from affecting you. For example, "The dog kept the strangers at bay." In this sentence, she was able to control her fears and not let them take over during the presentation — just like a castle keeps enemies at bay by holding them back!

Let's confirm by checking the other options:

• Keep off means to stay away from something physically, like "Keep off the grass!" Fears aren't something you physically stay away from.
• Back up means to support someone or move backward. Nothing to do with controlling fears.
• Put down means to place something on a surface or to criticize someone. Doesn't fit the meaning of holding back fears.

Hence, Keep at bay is the correct answer.