The quadratic function is an important concept for calculus but the students at high school have many difficulties related to this concept. It is important that the teaching of the quadratic function is realized considering the students' thinking. In this context, the aim of this study conducted through a qualitative case study is to reveal the concepts in a student's mind and their underlying reasons while he was analyzing a quadratic function and drawing its graph. While collecting the data, a clinical interview was conducted with Ozgur studying at Grade 11 and the interview was recorded with a camera. Then, the video camera records were verbatim transcribed for revealing Ozgur's thoughts related to the quadratic functions. At the beginning of the clinical interview, he tried to remember his existing knowledge but he could not be successful. He expressed that the given quadratic function was a linear function. Also, he did not relate the algebraic representation to graphical representation although he thought that its graph was a parabola and the parabola was opening upwards or downwards. As the interview progressed, he began to reason the concept and its properties. With the researcher's questions during interview, he noticed his misunderstanding. He understood the difference between the linear function and the quadratic function. Also he inferred the axis of symmetry and its importance for the quadratic function. Reflection of these thoughts in the teaching of the quadratic functions and the tasks related to the concept is important for conceptual learning.