Sketching Quartic Graphs: Key Features | 四次函数图像：特征与绘图

📚 Sketching Quartic Graphs: Key Features | 四次函数图像：特征与绘图

A quartic function is a polynomial of degree four. Unlike linear or quadratic graphs, a quartic graph can take many different shapes, including W-shaped curves, M-shaped curves, and curves with turning points and inflections. In this article, we will study the key features of quartic graphs and learn a systematic method for sketching them.

四次函数是四次多项式。与一次或二次函数图像不同，四次函数图像可以呈现多种不同的形状，包括 W 形、M 形，以及带有极值点和拐点的曲线。在本文中，我们将研究四次函数图像的关键特征，并学习一种系统性的绘图方法。

1. Standard Form of a Quartic Function | 四次函数的标准形式

A general quartic function is written as

一般四次函数写作

f(x) = ax⁴ + bx³ + cx² + dx + e, a ≠ 0

where a, b, c, d, e are constants. The term ax⁴ is the leading term, and a is the leading coefficient.

其中 a、b、c、d、e 为常数。项 ax⁴ 是首项，a 是首项系数。

Because the degree is even, the graph has the same end behaviour on both sides. The sign of a alone decides whether both ends rise or fall.

由于次数为偶数，图像两端的端行为相同

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