GCSE Maths (AQA)

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Quadratic Inequalities

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Algebra Solving Equations and Inequalities

Quadratic Inequalities

7:38 Solving Inequalities
Spec A22
Previous Inequality Set Notation Next Graphing Inequalities
  • Graphs can be used to show when a quadratic is greater than or equal to zero
  • Quadratic equations follow the general form y = ax^2 + bx + c and can cross the x-axis at up to two points
  • Critical values of a quadratic inequality are the points where the quadratic is equal to zero
  • The solution to a quadratic inequality can be found by inspecting the graph or checking if a value between the critical values satisfies the inequality
  • The solution can be described using set notation, with the values of x that satisfy the inequality in either the first or last section of the graph
  • The solution needs to include the critical values themselves because the original inequality has a greater than or equal to symbol
  • To solve a quadratic inequality, find the critical values by solving the quadratic equation equal to zero
  • Factorization can be used to find the critical values
  • Test a value between the critical values to determine if the inequality is satisfied
  • The full solution is given by the values in the range between the critical values, using strict less than symbols since the original inequality used a strict less than symbol

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