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Other graphs - OCRCubic 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 graph is produced when you have an equation of the form \(y = ax^3 + bx^2 + cx + d\), where \(b\), \(c\) and \(d\) can be zero but \(a\) cannot be zero. Cubic graphs are curved but can have more than one change of direction.

Example

Draw the graph of \(y = x^3 - x + 8\)

Solution

First we need to complete our table of values:

\(\text{x}\)-3-2-10123
\(\text{y = x}^3-\text{x~+~8}\)
\(\text{x}\)
-3
-2
-1
0
1
2
3
\(\text{y = x}^3-\text{x~+~8}\)
  • when \(x = -3\), \(y = (-3 \times -3 \times -3) 鈥 (-3) + 8 = -16\)
  • when \(x = -2\), \(y = (-2 \times -2 \times -2) 鈥 (-2) + 8 = 2\)
  • when \(x = -1\), \(y = (-1 \times -1 \times -1) 鈥 (-1) + 8 = 8\)
  • when \(x = 0\), \(y = (0 \times 0 \times 0) 鈥 0 + 8 = 8\)
  • when \(x = 1\), \(y = (1 \times 1 \times 1) 鈥 1 + 8 = 8\)
  • when \(x = 2\), \(y = (2 \times 2 \times 2) 鈥 2 + 8 = 14\)
  • when \(x = 3\), \(y = (3 \times 3 \times 3) 鈥 3 + 8 = 32\)
\(\text{x}\)-3-2-10123
\(\text{y = x}^3-\text{x~+~8}\)-1628881432
\(\text{x}\)
-3
-2
-1
0
1
2
3
\(\text{y = x}^3-\text{x~+~8}\)
-16
2
8
8
8
14
32

The graph will then look like this:

A graph showing the equation y = x3 - x + 8
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Reciprocal graphs
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Quadratic graphs

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