Quadratic inequalities

• Solving quadratic inequalities


  1. Transform inequality into quadratic equation

  2. Solve quadratic equation by factoring

  3. Identify critical points

  4. Test points between critical points

  5. Determine if critical points are included or not based on inequality symbol

  6. Express solution in interval notation
• Quadratic inequality


  Inequality involving a quadratic expression
• Steps to solve quadratic inequality


  • Transform inequality into quadratic equation

  2. Solve quadratic equation by factoring

  3. Identify critical points (solutions of quadratic equation)

  4. Test points between critical points to determine if they satisfy the inequality

  5. Determine if critical points are included or not based on inequality symbol (less than, less than or equal to)

  6. Express solution in interval notation
• Solving example quadratic inequality

  Transform inequality into quadratic equation: x^2 + 3x - 10 = 0

  2. Solve quadratic equation by factoring: (x + 5)(x - 2) = 0, so x = -5 or x = 2

  3. Identify critical points: -5, 2

  4. Test point 0 between -5 and 2: (0 + 5)(0 - 2) = -10 < 0, so 0 satisfies the inequality

  5. -6 is less than -5, so -6 does not satisfy the inequality

  6. 3 is greater than 2, so 3 does not satisfy the inequality

  7. Express solution in interval notation: (-5, 2)
• Students are asked to solve this new quadratic inequality and express the solution in interval notation