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Maths

Cubic graphs and graphs of circles - Higher

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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

×−3−2−10123
y = x3 - x + 8−1628881432
image: graph for the equation y = x to the power of 3 minus x + 8

You could be asked to solve equations using a graph.

Question

Solve the equation x3 + x2 - 12 = 0 using a graph.

toggle answer

Answer
  • x3 + x2 - 12 = 0
  • When the graph crosses y the axis
image: graph for the equation y = x to the power of 3 + x to the power of 2 minus 12

  • 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. The graph below shows the equation y = -x3.

image: graph for the equation y = minus x to the power of 3

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