For a cubic, factorise where possible to find x-intercepts, then consider the leading term to decide the ends. With a positive cubic coefficient the left end falls and the right end rises. A negative coefficient reverses this. Example y=x3-4x=x(x-2)(x+2) crosses the x-axis at -2,0,2. It has origin symmetry because replacing x by −x changes y to −y. By contrast, y=x3+2 is increasing throughout and crosses the y-axis at 2. Do not force two turning points into every cubic. A sketch should show the correct roots, intercepts and shape, even when it is not plotted to scale.

For a cubic, factorise where possible to find x-intercepts, then consider the leading term to decide the ends. With a positive cubic coefficient the left end falls and the right end rises. A negative coefficient reverses this.

\(y=x^3-4x=x(x-2)(x+2)\) crosses the x-axis at \(-2,0,2\). It has origin symmetry because replacing x by −x changes y to −y.

By contrast, \(y=x^3+2\) is increasing throughout and crosses the y-axis at 2. Do not force two turning points into every cubic. A sketch should show the correct roots, intercepts and shape, even when it is not plotted to scale.

Functions and Graphs

Cambridge IGCSE Mathematics 0580. Initial catalogue covers the assessed demands of February/March 2026 Paper 22; further Core and Extended mappings require paper-level scope review.

Cubic roots and overall shape

Cubic roots and overall shape