Chapter 1
Linear Equations and Graphing
Course: Gre
Subject: Gre Quantitative Reasoning
Chapter: Advanced Algebra And Systems Of Equations
Introduction: Multiple Ways to Express the Same Curve
Quadratic equations—the equations that produce parabolas—can be written in several different forms. Each form emphasizes different features of the parabola, making certain calculations easier depending on what information is needed.
Understanding how to recognize and convert between these forms equips mathematicians with flexibility in solving problems and interpreting graphs.
Three Forms of Quadratic Equations
Quadratic functions can be expressed in three main forms. Each form highlights different features of the parabola.
| Form | General Equation | Key Information Revealed | | Standard Form | f(x) = ax² + bx + c | y-intercept, opening direction | | Vertex Form | f(x) = a(x - h)² + k | Vertex, opening direction | | Intercept Form | f(x) = a(x - p)(x - q) | x-intercepts (roots), opening direction |