Chapter 1
Linear Equations and Graphing
Course: Gre
Subject: Gre Quantitative Reasoning
Chapter: Advanced Algebra And Systems Of Equations
Introduction: When Quadratics Hide
Not all quadratic equations are presented neatly in the form ax² + bx + c = 0. Sometimes they appear with parentheses, terms on both sides, or other complications. The key is to recognize that any equation that can be rearranged into standard form is a quadratic equation.
This lesson explores how to identify and solve quadratic equations that are not initially in standard form.
The Goal: Standard Form
The standard form of a quadratic equation is:
ax² + bx + c = 0
Once an equation is in this form, we can solve it by factoring, completing the square, or using the quadratic formula.
Step-by-Step Process
| Step | Action | | 1 | Distribute any terms and eliminate parentheses | | 2 | Move all terms to one side of the equation (set equal to zero) | | 3 | Combine like terms | | 4 | Arrange terms in descending order (ax² + bx + c) | | 5 | Solve using appropriate method |