Assess students' ability to analyze how the coefficients a, b, and c in y = ax^2 + bx + c affect parabola orientation and width, determine the vertex and axis of symmetry (using -b/(2a) and completing the square), predict number and nature of roots via the discriminant Δ = b^2 − 4ac, and explain how systematic changes to coefficients shift or reshape the graph; include numerical and conceptual tasks of moderate difficulty suitable for Grades 9–12.