Chapter 1
Linear Equations and Graphing
Course: Gre
Subject: Gre Quantitative Reasoning
Chapter: Advanced Algebra And Systems Of Equations
Introduction: Finding the Zeros
Quadratic equations arise whenever a quadratic function crosses the x-axis. Solving these equations—finding the x-values where the function equals zero—is a fundamental skill in algebra.
While some quadratic equations factor easily, others require more advanced methods. This lesson covers three primary approaches: factoring, completing the square, and the quadratic formula.
What Is a Quadratic Equation?
A quadratic equation is an equation where the highest exponent of the variable is 2. The standard form is:
ax² + bx + c = 0
Where a, b, and c are real numbers, and a ≠ 0 (if a = 0, the equation becomes linear).
Identifying Quadratic Equations
An equation is quadratic if:
- All exponents of the variable are nonnegative integers
- The highest exponent is 2
Examples: