Graphing and Solving Quadratic Functions

Miacademy & MiaPrep Learning Channel

This educational video uses the real-world scenario of a diving competition to explain the properties and applications of quadratic functions. The video begins by modeling a diver's trajectory using a specific equation, challenging viewers to identify the correct graph that represents the dive based on concepts like x-intercepts and concavity. It effectively transitions from this concrete application to abstract algebraic problem-solving techniques. Key mathematical themes include analyzing parabolas, finding x-intercepts (also called roots or zeros), calculating the time interval between two intercepts, and utilizing the quadratic formula. The video provides a detailed explanation of the discriminant ($b^2 - 4ac$), demonstrating how it predicts the number and type of roots (real vs. imaginary) a function possesses. It also touches upon advanced concepts such as complex numbers and root multiplicity. This resource is highly valuable for algebra classrooms as it bridges the gap between theoretical math and physical motion. Teachers can use it to introduce quadratic modeling, reinforce the relationship between algebraic equations and their graphical representations, or as a comprehensive review of solving quadratics using factoring and the quadratic formula. The step-by-step walkthroughs of different problem types allow for paused learning and immediate practice.