The teacher gives the class twelve quadratics, from x² + 5x + 6 = 0 to 2x² − 7x + 3 = 0, and students solve each by factorising in their books. After each one they type the quadratic into the Desmos graphing calculator and check whether the graph crosses the x-axis at their roots. When the graph disagrees, students find their own error before moving on and note what went wrong: a sign slip, a wrong factor pair or forgetting to set each bracket equal to zero. The teacher collects the most common slips at the end and sets two extra questions targeting them, including x² + 2x + 5 = 0, whose graph never crosses the axis, to open a discussion of quadratics with no real roots.
This page is one of a growing set of PICRAT examples by cell, subject and grade. Page maintained by Andy Perryer.