📚 Quadratic Equations: A Complete Guide for IGCSE Mathematics | 二次方程：IGCSE数学完全指南
Quadratic equations are one of the most important topics in IGCSE Mathematics. They appear in almost every paper, from simple factorisation questions to complex word problems. This guide covers every method you need to know, common pitfalls, and exam strategies to help you secure full marks.
二次方程是IGCSE数学中最重要的内容之一。几乎每张试卷都会出现，从简单的因式分解题到复杂的应用题。本指南涵盖你需要掌握的每一种解法、常见陷阱以及考试策略，助你稳拿满分。
1. Understanding Quadratic Equations | 理解二次方程
A quadratic equation is an equation where the highest power of the variable is 2. The general form is ax² + bx + c = 0, where a ≠ 0, and a, b, c are constants. For example, 2x² + 5x – 3 = 0 is a quadratic equation, while x³ + 2x = 1 is not.
二次方程是指变量最高次数为2的方程。一般形式为 ax² + bx + c = 0，其中 a ≠ 0，a、b、c 为常数。例如，2x² + 5x – 3 = 0 是二次方程，而 x³ + 2x = 1 不是。
The curve produced by a quadratic function y = ax² + bx + c is called a parabola. When a > 0, the parabola opens upward (U-shaped); when a < 0, it opens downward (n-shaped). The solutions of the equation, also called roots or x-intercepts, are the x-values where the parabola crosses the x-axis.
二次函数 y = ax² + bx + c 所绘制的曲线称为抛物线。当 a > 0 时，抛物线开口向上（U形）；当 a < 0 时，开口向下（n形）。方程的解也称为根或 x 轴截距，是抛物线与 x 轴相交处的 x 值。
2. Standard Form and Key Terms | 标准形式与关键术语
Before solving any quadratic equation, always rearrange it into the standard form ax² + bx + c = 0. This means moving all terms to one side, leaving zero on the other. For instance, 3x² + 7 = 5x becomes 3x² – 5x + 7 = 0.
在解任何二次方程之前，务必先将其整理为标准形式 ax² + bx + c = 0。这意味着将所有项移到等号一边，使另一边为零。例如，3x² + 7 = 5x 应整理为 3x² – 5x + 7 = 0。
Key terms to remember:
需要记住的关键术语：
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Coefficient (系数): the number multiplying the variable, such as 3 in 3x².
系数：
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