Magnetic resonance imaging (MRI) offers superior soft tissue contrast and is widely used in biomedicine. However, conventional MRI is not quantitative, which presents a bottleneck in image analysis and digital healthcare. Typically, additional scans are required to disentangle the effect of multiple parameters of MR and extract quantitative tissue properties. Here we investigate a data-driven strategy Q^2 MRI (Qualitative and Quantitative MRI) to derive quantitative parametric maps from standard MR images without additional data acquisition. By taking advantage of the interdependency between various MRI parametric maps buried in training data, the proposed deep learning strategy enables accurate prediction of tissue relaxation properties as well as other biophysical and biochemical characteristics from a single or a few images with conventional T_1/T_2 weighting. Superior performance has been achieved in quantitative MR imaging of the knee and liver. Q^2 MRI promises to provide a powerful tool for a variety of biomedical applications and facilitate the next generation of digital medicine.