Quartic Graphs | 四次函数图像

📚 Quartic Graphs | 四次函数图像

Quartic graphs are the graphs of polynomial functions of degree four. In A-Level Mathematics, especially Edexcel, you need to sketch these curves, identify their key features, and understand how repeated factors affect the shape. This article covers the essential ideas and exam techniques for quartic graphs.

四次函数图像是四次多项式函数的图像。在 A-Level 数学（尤其是 Edexcel 考试局）中，你需要会画出这些曲线、识别图像的关键特征，并理解重因式如何影响图像形状。本文涵盖四次函数图像的核心概念与考试技巧。

1. What is a quartic? | 什么是四次函数

A quartic function has the general form y = ax⁴ + bx³ + cx² + dx + e, where a, b, c, d and e are constants and a ≠ 0. The highest power of x is 4, so it is called a quartic or degree-four polynomial.

四次函数的一般形式为 y = ax⁴ + bx³ + cx² + dx + e，其中 a、b、c、d、e 为常数，且 a ≠ 0。x 的最高次数为 4，因此称为四次函数或四次多项式。

Its domain is all real numbers. Unlike quadratics, a quartic can have up to four real roots and up to three stationary points, so its graph can show more varied shapes than a quadratic or cubic graph.

它的定义域为全体实数。与二次函数不同，四次函数最多可有四个实根和三个驻点，因此图像形状比二次或三次函数

Published by TutorHao | A-Level Mathematics Revision Series | aleveler.com

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