Quadratic Equations for IGCSE Mathematics | IGCSE 数学二次方程精讲

📚 Quadratic Equations for IGCSE Mathematics | IGCSE 数学二次方程精讲

Quadratic equations appear in nearly every IGCSE Mathematics paper, from solving simple factorised forms to sketching graphs and applying quadratics in real-world problems. This revision guide brings together the essential methods, key formulas, graph interpretations and common errors in one place.

二次方程几乎出现在每一套 IGCSE 数学试卷中，包括简单的因式分解求解、图像草图以及二次函数在实际问题中的应用。本复习指南将核心方法、关键公式、图像解读和常见错误集中讲解，帮助考生系统掌握。

1. What Is a Quadratic Equation? | 什么是二次方程？

A quadratic equation in one unknown is an equation that can be written in the form ax² + bx + c = 0, where a, b and c are constants and a ≠ 0. The highest power of the unknown x is 2, which gives the equation its name.

一元二次方程是指可以写成 ax² + bx + c = 0 形式的方程，其中 a、b、c 是常数且 a ≠ 0。未知数 x 的最高次数为 2，因此称为二次方程。

For example, x² + 5x + 6 = 0, 2x² − 3x + 1 = 0 and x² − 9 = 0 are all quadratic equations. If a = 0, the equation becomes linear, so the condition a ≠ 0 is essential.

例如，x² + 5x + 6 = 0、2x² − 3x + 1 = 0 和 x² − 9 = 0 都是二次方程。如果 a = 0，方程就变成一次方程，因此 a ≠ 0 这个条件非常重要。

2. Standard Form and Key Terms | 标准形式与关键术语

Before solving, always rearrange the equation into standard form ax² + bx + c = 0. Bring all terms to one side and

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