Solving Quadratic Equations: Factorising, Completing the Square and the Quadratic Formula | 二次方程求解：因式分解、配方法与求根公式

📚 Solving Quadratic Equations: Factorising, Completing the Square and the Quadratic Formula | 二次方程求解：因式分解、配方法与求根公式

Quadratic equations appear throughout the IGCSE syllabus, from algebraic manipulation to real-world modelling. This revision guide covers the three main algebraic methods for solving quadratics, the role of the discriminant, and how the solutions connect to the graph of a parabola.

二次方程贯穿 IGCSE 数学大纲，从代数运算到实际建模都会出现。本复习指南涵盖求解二次方程的三种主要代数方法、判别式的作用，以及方程的解与抛物线图像之间的联系。

1. Recognising a Quadratic Equation | 识别二次方程

A quadratic equation is any equation that can be rearranged into the form ax² + bx + c = 0, where x is the variable and a, b, c are constants with a not equal to 0. The key feature is the x² term, which makes the relationship non-linear.

二次方程是任何可以整理为 ax² + bx + c = 0 形式的方程，其中 x 是变量，a、b、c 是常数，且 a 不等于 0。关键特征是含有 x² 项，这使关系成为非线性。

This means equations such as 2x² − 7 = 0, x² + 4x = 1, and (x − 3)(x + 2) = 0 are all quadratics. However, 5x + 3 = 0 is linear because the highest power of x is 1.

这意味着诸如 2x² − 7 = 0、x² + 4x = 1 以及 (x − 3)(x + 2) = 0 的方程都是二次方程。而 5x + 3 = 0 是一次方程，因为 x 的最高次数是 1。

In IGCSE questions, quadratics often appear after expanding brackets or rearranging terms. Identifying the equation type early helps you choose the most efficient solving strategy.

在 IGCSE 题目中，二次方程经常在展开括号或移项后出现。尽早识别方程类型有助于你选择最高效的求解策略。

2. The Standard Form ax² + bx + c = 0 | 标准形式 ax² + bx + c = 0

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