Equations of curves - Intermediate & Higher tier – WJECCubic graphs - Higher only

Quadratic, cubic and exponential graphs are three different types of curved graphs. We can use them to solve equations relating to the graph.

Part ofMathsAlgebra

Cubic graphs - Higher only

A cubic graph is any graph which has an \(\text{x}^3\) in its equation. Cubic graphs are still curved but can have more than one change of direction in them.

Example

Let’s draw the graph of \(\text{y = x}^3-\text{x + 8}\).

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 x -3 x -3) – (-3) + 8 = -16
  • when x = -2, y = (-2 x -2 x -2) – (-2) + 8 = 2
  • when x = -1, y = (-1 x -1 x -1) – (-1) + 8 = 8
  • when x = 0, y = (0 x 0 x 0) – 0 + 8 = 8
  • when x = 1, y = (1 x 1 x 1) – 1 + 8 = 8
  • when x = 2, y = (2 x 2 x 2) – 2 + 8 = 14
  • when x = 3, y = (3 x 3 x 3) – 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

Question

Complete the table and draw the graph of \(\text{y = x}^3+\text{x}^2-\text{12}\).

\(\text{x}\)-3-2-10123
\(\text{y = x}^3+\text{x}^2-\text{12}\)
\(\text{x}\)
-3
-2
-1
0
1
2
3
\(\text{y = x}^3+\text{x}^2-\text{12}\)

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Quadratic graphs - Intermediate and Higher tier

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