Mastering Quadratic Equations | 掌握二次方程

📚 Mastering Quadratic Equations | 掌握二次方程

Quadratic equations appear throughout the IGCSE Mathematics syllabus, from pure algebra questions to graphs, geometry and real-life problem solving. A confident grasp of this topic can earn you many reliable marks, so it is worth mastering every method carefully.

二次方程贯穿 IGCSE 数学考纲的各个部分，既出现在纯代数题中，也出现在函数图像、几何和实际应用题里。扎实掌握这一专题能为你带来许多稳定的分数，因此值得认真掌握每一种解法。

1. Standard Form and Key Definitions | 标准形式与核心概念

A quadratic equation is any equation that can be written in the form ax² + bx + c = 0, where a, b and c are constants and a ≠ 0. The condition a ≠ 0 is essential: if a = 0, the x² term disappears and the equation becomes linear.

二次方程是可以写成 ax² + bx + c = 0 形式的方程，其中 a、b、c 为常数，且 a ≠ 0。条件 a ≠ 0 至关重要：若 a = 0，x² 项消失，方程就退化为一次方程。

In IGCSE questions, you may need to expand brackets, collect like terms, or move all terms to one side before the equation is in standard form. Always take a moment to rearrange the equation before choosing a solution method.

在 IGCSE 题目中，你常常需要先展开括号、合并同类项，或者把所有项移到等号同一边，才能得到标准形式。选择解法之前，务必先花一点时间整理方程。