A GQF file is most commonly known as a GrafEq Data File, which is associated with GrafEq, a graphing and math visualization program developed by Pedagoguery Software Inc. It is not a common everyday file type like a PDF, Word document, image, or spreadsheet. Instead, it is a specialized file format mainly used by a specific graphing program. Because of this, Windows may not automatically know how to open it unless the proper software is installed.
A GQF file may contain graphing-related data used by GrafEq, such as mathematical formulas, equations, inequalities, graph settings, plotted graph information, and vector-style drawing data. In simple terms, it can be thought of as a saved graphing project file rather than a regular image. For example, instead of only storing a screenshot of a graph, the file may store the actual formula or mathematical relationship used to create the graph. This allows the program to reopen the file, redraw the graph, and possibly let the user edit the formula or settings.

In simple terms, a GQF file is most likely a saved GrafEq graphing file. It is used to store math graphing data, such as formulas and graph settings, rather than ordinary text or images. If it does not open, the issue is usually that the correct software is missing, the file association is wrong, the file is corrupted, or the file is not actually a valid GQF file.