In this study, we aimed to implement a learning system that supports learners to solve problems with respect to `Existence Domain of Solutions of Quadratic Functions (EDSQF)'. Our system also supports them to relearn previous units of quadratic functions. In addition, we designed a method for estimating learners' weak points with their use histories on our system. In our system, learners can learn by using learning materials with respect to EDSQF and related units. Our system has a function that checks learners' answers automatically and a function that provides explanations. Namely, learners can recognize immediately whether their answer is correct or not. Moreover, if they failed to solve problems, they can find explanations of those problems and challenge to solve related exercises. By providing these functions, learners can do self-learning with our system. Experimental results are proved that our system had a positive effect on learning EDSQF and related units to solve problems.