Quadratic Functions and Graphs | 二次函数与图像

📚 Quadratic Functions and Graphs | 二次函数与图像

Quadratic functions are polynomial functions of degree two. They appear throughout IGCSE Mathematics, from basic algebra to coordinate geometry and practical problem solving. Mastering their graphs and solving equations is essential for exam success.

二次函数是二次多项式函数。它们贯穿 IGCSE 数学的始终，从基础代数到坐标几何，再到实际问题的求解。掌握它们的图像和方程求解对考试成功至关重要。

1. What is a Quadratic Function? | 什么是二次函数？

A quadratic function is any function that can be written in the general form:

二次函数是任何可以写成一般形式的函数：

f(x) = ax² + bx + c, where a ≠ 0

Here a, b and c are constants. The coefficient a cannot be zero because if a = 0, the function reduces to a linear function, not a quadratic one.

其中 a、b 和 c 是常数。系数 a 不能为零，因为如果 a = 0，函数就会退化为线性函数，而不是二次函数。

The graph of a quadratic function is a smooth curve called a parabola. When a > 0, the parabola opens upward like a “U”; when a < 0, it opens downward like an upside-down "U". Understanding this simple fact helps you quickly predict the shape of the graph.

二次函数的图像是一条光滑的曲线，称为抛物线。当 a > 0 时，抛物线开口朝上，形如“U”；当 a < 0 时，抛物线开口朝下，形如倒“U”。理解这个简单事实有助于你迅速判断图像的基本形状。

2. Key Features of the Graph | 图像的关键特征

The graph of f(x) = ax² + bx + c has several important

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