Most students learn to solve quadratic equations by factoring, completing the square, or using the quadratic formula. But what if there were another way to solve quadratics using something you already know—the axis of symmetry?
In this video, you’ll learn Po-Shen Loh’s method for solving quadratic equations, an alternative approach that uses the relationship between the roots of a quadratic equation. Rather than relying on memorized formulas, this method builds on the axis of symmetry, the sum of the roots, and the product of the roots to find solutions.
We’ll walk through the process step by step, showing how to set up the roots, multiply the resulting binomials, and solve for the unknown value to determine both solutions.
In this lesson you’ll learn:
• What Po-Shen Loh’s method is and how it works
• How the axis of symmetry relates to the roots of a quadratic equation
• Why the roots can be written as (-b/2+u) and (-b/2-u)
• How to use the sum and product of the roots
• How to set up an equation using two binomial expressions
• How multiplying conjugates helps simplify the equation
• How to solve for u to find both roots
• How this method connects to traditional quadratic-solving techniques
• Why understanding the structure of quadratic equations is more valuable than simply memorizing formulas
By the end of this lesson, you’ll understand how Po-Shen Loh’s method works and how to use it to solve quadratic equations without directly applying the quadratic formula.
Whether you’re taking Algebra 1, Honors Algebra 2, Precalculus, or preparing for the ACT or SAT, understanding different approaches to solving quadratics can strengthen your algebra skills and mathematical reasoning.
