Solving Quadratic Equations: Factorising, Formula and Graphs | 解二次方程：因式分解、公式与图像

📚 Solving Quadratic Equations: Factorising, Formula and Graphs | 解二次方程：因式分解、公式与图像

Quadratic equations appear throughout the IGCSE Mathematics syllabus, from algebraic manipulation to real-world modelling. 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. Mastering this topic means knowing how to solve quadratics by factorising, completing the square, using the quadratic formula, and interpreting graphs. In this revision guide, we will break down each method step by step, highlight common mistakes, and show how exam questions are structured.

二次方程贯穿 IGCSE 数学课程，从代数运算到实际建模都有出现。二次方程是任何可以写成 ax² + bx + c = 0 形式的方程，其中 a、b、c 为常数且 a ≠ 0。掌握这一主题意味着要会通过因式分解、配方法、二次公式和图像解读来求解。在本复习指南中，我们将逐步拆解每种方法，指出常见错误，并说明考试题的结构。

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

A quadratic equation is a polynomial equation of degree 2. The highest power of the variable x is 2, and the equation can have two real solutions, one repeated solution, or no real solutions depending on the discriminant. The general form is shown below.

二次方程是一个次数为 2 的多项式方程。变量 x 的最高次数为 2，根据判别式的不同，方程可能有两个实

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