📚 Quadratic Equations: Factorising, Completing the Square and the Quadratic Formula | IGCSE数学二次方程：因式分解、配方法与求根公式
Quadratic equations are one of the most important topics in the IGCSE Mathematics syllabus. They appear in algebra, graphing, and real-world problems such as area, projectile motion, and profit calculations. In this article, we will work through the three main solution methods—factorising, completing the square, and the quadratic formula—and connect them to the graph of a quadratic function.
二次方程是 IGCSE 数学大纲中最重要的专题之一。它们出现在代数、函数图像以及面积、抛体运动和利润计算等实际问题中。本文将逐一讲解三种主要解法——因式分解法、配方法和求根公式法——并将它们与二次函数的图像联系起来。
1. What is a Quadratic Equation? | 什么是二次方程？
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 because if a were equal to zero, the x² term would disappear and the equation would become linear, not quadratic.
二次方程是任何可以写成 ax² + bx + c = 0 形式的方程，其中 a、b 和 c 是常数，并且 a ≠ 0。a ≠ 0 这个条件非常重要，因为如果 a 等于 0，x² 项就会消失，方程就变成一次方程，而不是二次方程。
For example, x² − 5x + 6 = 0 is quadratic because the highest power of x is 2. Equations such as 3x² = 12 or (x − 2)(x + 3) = 0 are also quadratic once they are expanded or rearranged.
例如，x² − 5x + 6 = 0 是二次方程，因为 x 的最高次数是 2。像 3x² = 12 或 (x − 2)(x + 3) = 0 这样的方程在展开或移项后也都是二次方程。
2. Standard Form and Key Terms | 标准形式与关键术语Published by TutorHao | IGCSE Mathematics Revision Series | aleveler.com
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