Mastering Quadratic Equations | 掌握二次方程

📚 Mastering Quadratic Equations | 掌握二次方程

Quadratic equations are one of the most frequently tested topics in Edexcel IGCSE Mathematics. They appear as pure algebra questions, as graph work, and inside geometry and problem-solving questions. This article gives a clear revision route through factorising, completing the square, the quadratic formula, the discriminant and quadratic graphs.

二次方程是 Edexcel IGCSE 数学中最高频的考点之一。它不仅出现在纯代数题中，也会作为函数图像、几何题和应用题的一部分。本文将以清晰的复习路径，带你掌握因式分解法、配方法、求根公式、判别式以及二次函数图像。

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

A quadratic equation is an equation in which the highest power of the unknown is 2. It can be written in the standard form shown below.

二次方程是未知数最高次数为 2 的方程。它通常可以写成下面的标准形式。

ax² + bx + c = 0, a ≠ 0

Here a, b and c are constants, with a not equal to zero. If a were zero, the equation would become linear because the x² term would disappear.

这里 a、b、c 都是常数，且 a 不等于 0。如果 a = 0，x² 项就会消失，方程就变成一次方程了。

For example, x² – 5x + 6 = 0, 2x² = 8 and x(x – 3) = 0 are all quadratic equations.

例如

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