OML Search

Graphs of Cubic Functions




In these lessons, we will learn

  • how to graph of cubic functions by plotting points.
  • how to graph cubic functions of the form y = a(xh)3 + k.

Related Topics: More Geometry Lessons

Plotting Points

The general form of a cubic function is y = ax3 + bx + cx + d where a , b, c and d are real numbers and a is not zero.

We can graph cubic functions by plotting points.

Example:

Draw the graph of y = x3 + 3 for –3 ≤ x ≤ 3. Use your graph to find
a) the value of y when x = 2.5
b) the value of x when y = –15

Solution:

x

–3

–2

–1

0

1

2

3

y

–24

–5

2

3

4

11

30

 

a) When x = 2.5, y 18.6

b) When y = –15, x –2.6



 

Example:

Plot the graph of y = x3 – 9x + 5 for –4 ≤ x ≤ 4 and use your graph to find:
a) the value of y when x = 1.6
b) the value of x when y = 12

Solution:

x

–4

–3

–2

–1

0

1

2

3

4

y

–23

5

15

13

5

–3

–5

5

33

 

a) When x = 1.6, y –5.3

b) When y = 12, x –0.8, or x –2.5



 


Graphing Cubic Functions

This video provides and example of how to graph a cubic or degree 3 polynomial function by completing a table of values.




 

Graph cubic functions of the form y = a(xh)3 + k.

We can graph cubic functions by transforming the basic cubic graph. The basic cubic graph is y = x3.

For the function of the form y = a(xh)3 + k.
If k > 0, the graph shifts k units up; if k < 0, the graph shifts k units down.
If h > 0, the graph shifts h units to the right; if h < 0, the graph shifts h units left.
If a < 0, the graph is flipped.

The following video shows how to graph cubic functions by writing the function in the form y = a(xh)3 + k.


How to graph a Transformation of a Cubic Function.





Basic introduction into graphing cubics - Part A


Basic introduction into graphing cubics - Part B




 

You can use the Mathway widget below to practice Algebra or other math topics. Try the given examples, or type in your own problem. Then click "Answer" to check your answer.

OML Search

We welcome your feedback, comments and questions about this site or page. Please submit your feedback or enquiries via our Feedback page.

[?] Subscribe To This Site

XML RSS
follow us in feedly
Add to My Yahoo!
Add to My MSN
Subscribe with Bloglines



Math TutorsMath Tutors