Cubic graphs

A cubic equation contains only up to and including \(x^3\). Here are some examples of cubic equations:

\(y = x^3\)

\(y = x^3 + 5\)

Cubic graphs are curved but can have more than one change of direction.

Example

Draw the graph of \(y = x^3\).

Solution

First complete a table of values:

\(\text{x}\)	-2	-1	0	1	2
\(y = x^3\)

\(\text{x}\)

-2

-1

0

1

2

\(y = x^3\)

when \(x = -2\), \(y = (-2 \times -2 \times -2) = -8\)
when \(x = -1\), \(y = (-1 \times -1 \times -1) = -1\)
when \(x = 0\), \(y = (0 \times 0 \times 0) = 0\)
when \(x = 1\), \(y = (1 \times 1 \times 1) = 1\)
when \(x = 2\), \(y = (2 \times 2 \times 2) = 8\)

\(\text{x}\)	-2	-1	0	1	2
\(y = x^3\)	-8	-1	0	1	8

\(\text{x}\)

-2

-1

0

1

2

\(y = x^3\)

-8

-1

0

1

8

The graph will then look like this:

Draw the graph of \(y = x^3 + 5\).

Solution

First complete a table of values:

\(\text{x}\)	-2	-1	0	1	2
\(y = x^3 + 5\)

\(\text{x}\)

-2

-1

0

1

2

\(y = x^3 + 5\)

when \(x = -2\), \(y = (-2 \times -2 \times -2) + 5 = -3\)
when \(x = -1\), \(y = (-1 \times -1 \times -1) + 5 = 4\)
when \(x = 0\), \(y = (0 \times 0 \times 0) = 0 + 5 = 5\)
when \(x = 1\), \(y = (1 \times 1 \times 1) = 1 + 5 = 6\)
when \(x = 2\), \(y = (2 \times 2 \times 2) = 8 + 5 = 13\)

\(\text{x}\)	-2	-1	0	1	2
\(y = x^3 + 5\)	-3	-4	5	6	13

\(\text{x}\)

-2

-1

0

1

2

\(y = x^3 + 5\)

-3

-4

5

6

13

The graph will then look like this:

Cubic graph of y = x to the power of 3 plus 5

Welcome to My Bitesize, let's get you set up!

Other Graphs - EduqasCubic graphs

Cubic graphs

Example

Solution

Solution

More guides on this topic

Related links