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Curve Sketching

Follow these steps for sketching a curve.

  1. Identify the general shape of the curve and whether it is of a negative or positive shape.
  2. Identify the y-intercept – substitute x=0 into the equation of the graph to see where the graph cuts the y-axis.
  3. Identify the roots of the cubic – this is where the graph should cut the x-axis. This may involve factorising and you should note that the graph will bounce off the x-axis at any repeated roots.
  4. Place the curve so that it cuts the x and y axes at the correct points making sure that the curve touches the x axis at any repeated roots.


In the simpler cases, you will typically be expected to draw quadratics, cubics and reciprocal functions. You may also be required to perform transformations of a given curve and you should also know how to sketch the reciprocal functions. Practice sketching cubics, transformations and reciprocal functions below.

See Completing the Square to find out how to sketch a quadratic. See Cubics to find out more about sketching cubics.