Paper 1 · Algebra ⏱ Tested in 4 exam questions since 2017 Lesson 9 of 23

Algebra 9 – Nature of quadratic graphs

You’ll learn

  • Compute the discriminant b² − 4ac and link its sign to the nature of the roots
  • Match exam wording — distinct, equal, real, no real — to >, =, ≥, <
  • Turn a nature-of-roots condition into an equation or inequality in k or t
  • Finish discriminant conditions with a t² term using the parabola-sketch method

Formula used

Roots of the quadratic equation

x = (-b ± √(b² − 4ac)) / 2a

On page 20 of the log tables — read it off, don’t memorise.

Most recent exam questions

  • 2025 P1 Q6(b)(i)
  • 2022 P1 Q1(a)
  • 2022 P1 Q1(b)
  • 2020 P1 Q1(a)(iii)
  • 2017 P1 Q1(c)(i)
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