Using the Discriminant to Predict Quadratic Solutions

Miacademy & MiaPrep Learning Channel

This Algebra video tutorial introduces students to the discriminant, a powerful component of the quadratic formula used to determine the number of real solutions for a quadratic equation. The narrator, Justin, builds upon previous knowledge of the quadratic formula to isolate the expression under the radical ($b^2 - 4ac$), explaining its specific function as a predictive tool. By breaking down the formula visually, the video helps students understand not just how to calculate the discriminant, but why it works mechanically within the larger equation. The content systematically explores the three possible outcomes of the discriminant calculation: positive, negative, and zero. Through clear visual aids and logical explanations, students learn that a positive result indicates two real solutions, a negative result means no real solutions exist, and a zero result yields exactly one real solution. The video reinforces these concepts with three distinct examples—one for each scenario—walking viewers through the step-by-step substitution and simplification process required to reach a conclusion. For educators, this resource serves as an excellent bridge between introducing the quadratic formula and graphing quadratic functions. It emphasizes efficiency in problem-solving by showing students how to avoid unnecessary work when no solutions exist. The video includes a guided practice opportunity where students are encouraged to pause and try a problem on their own, making it an interactive tool suitable for flipped classrooms, homework support, or direct instruction in Algebra I or II courses.