Accelerating the acquisition of magnetic resonance imaging (MRI) is a challenging problem, and many works have been proposed to reconstruct images from undersampled k-space data. However, if the main purpose is to extract certain quantitative measures from the images, perfect reconstructions may not always be necessary as long as the images enable the means of extracting the clinically relevant measures. In this paper, we work on jointly predicting cardiac motion estimation and segmentation directly from undersampled data, which are two important steps in quantitatively assessing cardiac function and diagnosing cardiovascular diseases. In particular, a unified model consisting of both motion estimation branch and segmentation branch is learned by optimising the two tasks simultaneously. Additional corresponding fully-sampled images are incorporated into the network as a parallel sub-network to enhance and guide the learning during the training process. Experimental results using cardiac MR images from 220 subjects show that the proposed model is robust to undersampled data and is capable of predicting results that are close to that from fully-sampled ones, while bypassing the usual image reconstruction stage.