Key Features of Cubic Functions

Chapter 5.1
Graphs of Cubic Functions and Graphical Solutions

Lesson Objectives

In this Sub-Chapter, you will learn how to:

Draw and solve questions involving Cubic Graphs
of the form y = ax³.

1) Graphs of Cubic Functions

A cubic graph has a general form of y = ax³ , where a is the coefficient of the x³ term.

For example, the coefficient of the x³ term in y= 4x³ is 4.

Draw

Sketch the following graphs using Desmos / Geogebra:

y = x³
y = 2x³
y = 5x³

Multiple Choice

Based on your graphs, what happens to the shape of the graph as you

increase the coefficient of x³ ? (i.e. value of a increases from 1 to 2 to 5)

• Graph becomes wider

• Graph becomes narrower

Draw

Sketch the following graphs using Desmos / Geogebra:

y = -x³
y = -2x³
y = -5x³

Open Ended

How are the graphs with positive coefficients (2x³ , 5x³ ) different

from the graphs with negative coefficients (-2x³ , -5x³ )?

(Hint: From left to right, what do you notice, are the curves going upwards or downwards?)

​Explore more cubic graphs using Desmos by plotting the following:

Write down your observations about the graphs of a cubic function.

​From the above investigation, we see that the graph of a cubic function of the form
y = ax³ + bx² + cx + d would take the following shapes below:

Self-Directed Learning:
- Read through Worked Example 2 on page 120 of textbook.

- Attempt Practice Now 2 on page 121 of textbook on Graph Paper.

- Submit to your respective Maths Teachers on Monday (8th April 2024).