If you are taking the higher paper you may be asked questions about graphs of circles and cubic graphs.
Cubic graphs
The simplest cubic graph is the graph of y = x3
Any graph where the highest power is x3 will have a similar shape. In the exam you will have to plot points to draw the graph accurately.
Example
Calculate the points and then plot the graph for the equation y = x3 - x + 8
| × | −3 | −2 | −1 | 0 | 1 | 2 | 3 |
| y = x3 - x + 8 | −16 | 2 | 8 | 8 | 8 | 14 | 32 |
You could be asked to solve equations using a graph.
- Question
Solve the equation x3 + x2 - 12 = 0 using a graph.
- Answer
- x3 + x2 - 12 = 0
- When the graph crosses y the axis
- So x3 + x2 -12 = 0
- When x = 2
Remember that if the term in x3 is negative, the graph will be the other way up (it will be reflected in the x axis, as all the y values will now be negative). The graph below shows the equation y = -x3.
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