Quadratic Equations – AS Mathematics

Prerequisite Knowledge

  • Know the difference between an equation and an identity; argue mathematically to show algebraic expressions are equivalent, and use algebra to support and construct arguments and proofs
  • Simplify and manipulate algebraic expressions by factorising quadratic expressions of the form ax2 + bx + c.
  • Understand and use standard mathematical formulae; rearrange formulae to change the subject

Success Criteria

  • Success CriteriaIdentify and interpret roots, intercepts, turning points of quadratic functions graphically.
  • Deduce roots algebraically and turning points by completing the square.
  • Recognise, sketch and interpret graphs of quadratic functions
  • Solve quadratic equations (including those that require rearrangement) algebraically by:
    • factorising,
    • completing the square using the quadratic formula;
  • Find approximate solutions using a graph

Teaching Points

  • Students need to understand how the discriminator determines the number and types of roots for a quadratic function.
  • When solving quadratic equations involving inequalities arising from the discriminator students benefit from sketching the quadratic to correctly determine the range of solutions.
  • When solving quadratics ensure students are able to arrange the coefficients a and b, and constant c term in line with the general form as this helps with the manipulation.
  • Students should be able to derive the quadratic formula by completing the square of the general form.


  • Students often struggle manipulating quadratics when the x2 term is negative.
  • Some students are unclear on the conditions for the number of roots when finding the discriminator.
  • Students often resort to using the formula when solving quadratics when it is more appropriate and efficient to use completing the square.
  • When sketching quadratic functions with no real roots students often make mistakes by drawing the curve below y = 0.

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