Roots and Turning Points

GCSE(F) GCSE(H)

A quadratic function will contain a squared term, but will have no higher power. It will be in the shape of a parabola which is a curve that comes to a rounded point then turns to curve back again. The point at which it turns is a turning point, and this will be either a minimum or a maximum value.

It is necessary, when plotting quadratic graphs, to plot more than three points to establish the shape of the graph. The graph y = x² - 3 may be plotted using the following points:

The turning point for this graph is at (0, -3). The roots of the function are found when y = 0: in this instance there are two roots at -1.67 and +1.67 (to 2dp). For any quadratic there may be two roots, one root (actually the same root repeated), or no roots (the graph does not cross y = 0.

Exam Tip: draw graphs as accurately to obtain any turning points or roots.