The aim of this qualitative case study is twofold: 1) to analyze how an eleventh-grader, Min-Seon, conceive and represent a pattern of change between two varying quantities in a quadratic functional situation, and 2) further to help her form a concept of ``derivative`` as a tool to express the relationship with employing a concept of ``rate of change.`` The result indicates that Min-Seon was able to construct graphs of piecewise functions that take average rates of change as range of the functions, and managed to conjecture the derivative of a quadratic function, y=x ^{2}. In conclusion, we argue that covariational approach could not only facilitate students`` construction of an initial function concept, but also support their understanding of the concept of ``derivative.``