Assess students' understanding of how the discriminant and vertex form determine the number and nature of roots and the graph of a quadratic. Items should require: computing and interpreting the discriminant (b^2−4ac) to classify roots as two distinct real, one repeated, or complex; converting between standard and vertex form and using y = a(x−h)^2 + k to identify vertex, axis of symmetry, direction and relative width (via a), and y-intercept; predicting x-intercepts from the discriminant and vertex information; and sketching or describing graph behavior based on these analyses. Include symbolic work, parameter reasoning, and short graphing/interpretation tasks appropriate for Grades 9–12.