Chapter 1
Linear Equations and Graphing
Course: Gre
Subject: Gre Quantitative Reasoning
Chapter: Advanced Algebra And Systems Of Equations
Introduction: Converting to Vertex Form
The quadratic equation y = ax² + bx + c (standard form) is useful for many purposes, but it does not directly reveal the vertex of the parabola. The vertex form, y = a(x - h)² + k, does. Converting from standard form to vertex form is accomplished through a process called completing the square.
This lesson explains how to complete the square and how this technique helps find the vertex of a parabola.
The Perfect Square Trinomial Pattern
A perfect square trinomial is a quadratic that can be factored as a binomial squared:
(x + d)² = x² + 2dx + d² (x - d)² = x² - 2dx + d²
Notice the pattern: the constant term (d²) is the square of half the coefficient of x.