This math unit begins with introducing the basics of quadratic formulas, transitioning from naming and identifying their purposes to delving deeper into characteristics such as the discriminant and its implications on quadratic graphs and roots. Students start by linking quadratic equations to their respective formulas and understanding the functions they describe. The unit progresses to interpreting the discriminant values to analyze how they influence the graph's appearance, the nature of the roots, and the count of roots in quadratic equations, further evaluating whether these roots are real or complex. The exercises escalate to involve calculating specific aspects like the radical roots and the x-coordinate of the vertex using quadratic formulas. Towards the end, the unit focuses on the comprehensive application of quadratic discriminants, including identifying discriminant values from graphs and examining the consistency of root types according to discriminant values, reinforcing a deeper understanding of the interplay between quadratic equations, their graphs, discriminants, and roots.Skills you will learn include:
Topics are small, focused areas which build towards the greater unit's goals.