How to Convert Quadratic Equations Between Standard and Vertex Form

The Organic Chemistry Tutor

A concise and clear mathematics tutorial demonstrating how to convert quadratic functions between standard form and vertex form. The video uses a step-by-step algebraic approach to transform the equation $y = x^2 + 6x - 5$. The instructor introduces the method of "completing the square" to convert from standard to vertex form, highlighting a specific technique of adding and subtracting the square term on the same side of the equation to maintain balance. The video also covers how to verify the calculated vertex using the formula $x = -b/(2a)$, providing students with a method to check their work. In the second half, the process is reversed, showing how to expand a vertex form equation back into standard form using the FOIL method and combining like terms. This demonstrates the cyclical relationship between the two forms. This resource is highly valuable for high school Algebra students who often struggle with the mechanics of completing the square. It isolates the procedural skills without the distraction of complex real-world word problems, making it an excellent reference for learning the specific algorithms required for manipulating quadratic equations. Teachers can use this to model the specific syntax and structure of algebraic proofs.