Quadratic Equations and Graphs | 二次方程与图像

📚 Quadratic Equations and Graphs | 二次方程与图像

Quadratic equations appear year after year in IGCSE Mathematics papers. They test your algebraic manipulation, your number sense, and your ability to interpret graphs. In this article, we will break down the entire topic step by step, from the standard form to the most common exam traps.

二次方程在 IGCSE 数学考试中年年出现。它考查你的代数运算能力、数感以及解读图像的能力。在本文中，我们将一步步拆解这个主题，从标准形式到最常见的考试陷阱。

1. The Standard Form | 标准形式

Every quadratic equation can be written in the standard form:

每一个二次方程都可以写成标准形式：

ax² + bx + c = 0, where a ≠ 0

ax² + bx + c = 0，其中 a ≠ 0

Here, a is the coefficient of x², b is the coefficient of x, and c is the constant term. The value of a can never be zero, because if a = 0, the equation becomes linear and the x² term disappears.

这里，a 是 x² 的系数，b 是 x 的系数，c 是常数项。a 的值绝不能为零，因为如果 a = 0，方程就变成了一次方程，x² 项也就不存在了。

Example 1: Write 3x² + 2x – 5 = 0 in terms of a, b and c.

例 1：写出 3x² + 2x – 5 = 0 中的 a、b、c。

Here a = 3, b = 2 and c = -5. Note that the minus sign belongs to c, so c is negative. Keeping the correct sign is essential when you use the quadratic formula later.

这里 a = 3，b = 2，c = -5。注意负号属于 c，因此 c 是负数。保持正确的符号对之后使用求根公式至关重要。

2. Factorising Quadratics | 因式分解二次式

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