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The purpose of this study was to describe students' understanding of the graph of quadratic functions. In this study, APOS theory (Action, Process, Object and Schema) was used as a theoretical framework. The subjects of this study were two students at STKIP PGRI Bangkalan, one male and one female with equal mathematics abilities. Data collection techniques were written tests and semi-structured interviews. The data generated were analyzed through the stages of data reduction, data presentation and conclusion. The results showed that at the stage of the action, male subjects made the graphs of function directly in the Cartesian plane and determined the function formula used the general form of quadratic functions. While the female subject made a table that contains the coordinates of the points that meet the formula given before making a graph and determined the formula of a given graph used the general form of quadratic functions. At the process stage, the male subject explained that the process of drawing a graph of functions by drawing some numbers of points that meet the equation then connecting the points, whereas for determining the formula, the subject could not explain in detail. The female subject at the process stage explained the process of drawing a graph by determining the points of intersection between function and coordinate axis, finding several other points that meet the equation, determining the direction of the graph based on the coefficient of then drawing the graph. Whereas when determining the function formula, the female subject investigated the point intersection between the graph and the coordinate axis, the extrem point then substitutes the value in the general form of a quadratic function. At the object stage, male subjects made a graph  by shifting the top of the graph  to (0, -2) without looking for other points, but the subject not at the object stage when searching for quadratic function formulas. While female subjects are not at the object stage when drawing graphics, but subjects determined the function formula of the graph whose top point was shifted up by adding constants from the original graph function formula, this indicated the subject was at the object stage. The scheme of the two subjects described that the two subjects could not made a connection between two functions and two graph of functions.

APOS, Graph of function, Quadratic Function