Steps for curve sketching

Follow these steps for sketching a curve.

  1. Firstly, identify the general shape of the curve and whether it is of a negative or positive shape.
  2. Next, find the y-intercept – substitute x=0 into the equation of the graph to see where the graph cuts the y-axis.
  3. Then, 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. Finally, 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. 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.

Curve Sketching Exercises