Graphs of Cubic Functions



In this lesson, 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







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