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2. Quadratic functions

Syllabus
0606–2028–2029
Topic
2
Level
—

2.1. Find maximum and minimum values

  • Find the maximum or minimum value of the quadratic function f: x -> ax^2 + bx + c by completing the square or by differentiation.

2.2. Use vertex values to sketch or find range

  • Use the maximum or minimum value of f(x) to sketch y = f(x) or determine the range for a given domain.
  • Use correct notation to write a domain or range.

2.3. Use discriminant conditions

  • Know the conditions for f(x) = 0 to have two real roots, two equal roots or no real roots.
  • Relate the discriminant to the roots of the equation.
  • Apply the related conditions for a line to intersect a curve, be tangent to a curve or not intersect a curve.

2.4. Solve quadratic equations

  • Solve quadratic equations for real roots.
  • Use factorisation, the quadratic formula and completing the square.
  • The quadratic formula is given in the List of formulas.
  • On the calculator paper, correct answers are acceptable without working.

2.5. Solve quadratic inequalities

  • Find the solution set for quadratic inequalities graphically or algebraically.
  • Write solutions in the correct form, such as -3 < x < 4 or x < 1 or x > 6.

Objective notes

5 learning objectives
ConceptIGCSE Additional Math