Machine reading comprehension with unanswerable questions is a new challenging task for natural language processing. A key subtask is to reliably predict whether the question is unanswerable. In this paper, we propose a unified model, called U-Net, with three important components: answer pointer, no-answer pointer, and answer verifier. We introduce a universal node and thus process the question and its context passage as a single contiguous sequence of tokens. The universal node encodes the fused information from both the question and passage, and plays an important role to predict whether the question is answerable and also greatly improves the conciseness of the U-Net. Different from the state-of-art pipeline models, U-Net can be learned in an end-to-end fashion. The experimental results on the SQuAD 2.0 dataset show that U-Net can effectively predict the unanswerability of questions and achieves an F1 score of 71.7 on SQuAD 2.0.