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Other graphs - AQACubic graphs

The most commonly occurring graphs are quadratic, cubic, reciprocal, exponential and circle graphs. Their equations can be used to plot their shape.

Part of MathsAlgebra

Cubic graphs

A cubic equation contains only terms up to and including x鲁. 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 we need to complete our table of values:

\(x\)-2-1012
\(y = x^3\)
\(x\)
-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 \(x = 2\), \(y = (2 \times 2 \times 2) = 8\)
\(x\)-2-1012
\(y = x^3\)-8-1018
\(x\)
-2
-1
0
1
2
\(y = x^3\)
-8
-1
0
1
8

The graph will then look like this:

Cubic graph of y = x to the power of 3

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

Solution

First we need to complete our table of values:

\(\text{x}\)-2-1012
\(y = x^3 + 5\)
\(\text{x}\)
-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 \(x = 2\), \(y = (2 \times 2 \times 2) = 8 + 5 = 13\)
\(\text{x}\)-2-1012
\(y = x^3 + 5\)-345613
\(\text{x}\)
-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
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