Assess students' ability to analyze quadratic functions: use the discriminant to classify real, repeated, or complex roots; relate coefficients a, b, c to vertex coordinates and the axis of symmetry (including use of -b/2a and completing the square); convert between standard and vertex form; and predict how varying parameters a, b, and c changes graph shape, width, orientation, vertex position, and roots. Include calculation, interpretation, and short explanation tasks that require reasoning about transformations and root behavior.