Solving Quadratic Inequalities Worksheet

Solving quadratic inequalities at a glance

Quadratic inequalities are inequalities that involve a squared term. As with linear inequalities, there are four types: greater than >, less than <, greater than or equal to ≥ and less than or equal to ≤. 

To solve a quadratic inequality, we first write it as a quadratic equation by changing the inequality sign to an equals sign. We can then solve the quadratic equation either by factorising or using the quadratic formula. This tells us the roots of the equation, i.e. the values for which the expression is equal to 0.

Once we have the roots of the equation, we can sketch the quadratic function – this will be a parabola. We need to look for the x values which satisfy the inequality – if the inequality is > 0 then we are looking for the x values for which the graph is above the x axis and if it is < 0 then we are looking for the x values where the graph is below the x axis.

Looking forward, students can progress with more inequalities worksheets, to additional algebra worksheets, for example a simplifying expressions worksheet, factorising worksheet or simultaneous equations worksheet.

For more teaching and learning support on Algebra our GCSE maths lessons provide step by step support for all GCSE maths concepts.