This article presents secondary students' generalizations about the connections between algebraic and graphical representations of quadratic functions, focusing specifically on the roles of the parameters a, b, and c in the general form of a quadratic function, y = ax[superscript 2] + bx + c. Students' generalizations about these connections led to a surprising finding: two-thirds of the students interviewed identified the parameter a as the "slope" of the parabola. Analysis of qualitative data from interviews and classroom observations led to the development of three "focusing phenomena" in the classroom environment that inadvertently supported a focus on slope-like properties of quadratic functions: (a) the use of linear analogies, (b) the rise over run method, and (c) viewing "a" as dynamic rather than static. (Contains 10 figures and 1 table.)