Quadratic Equations
Term 2
Factorising · Completing the square · Quadratic formula
Learning Objectives
PrintSolving Quadratic Equations
- 1. Solve a quadratic equation by factorising and applying the null factor law.
- 2. Solve a quadratic equation of the form $x^2 = k$ or $(x - a)^2 = k$.
- 3. Solve rational equations that reduce to a quadratic after clearing fractions.
- 4. Complete the square to solve a quadratic equation.
- 5. Solve a quadratic equation using the quadratic formula $x = \dfrac{-b \pm \sqrt{b^2 - 4ac}}{2a}$.
- 6. Give exact (surd) solutions to quadratic equations where appropriate.
Graphs of Quadratic Functions
- 7. Identify the $y$-intercept of a quadratic function as $f(0)$.
- 8. Find the $x$-intercepts (roots) of a quadratic by setting $f(x) = 0$.
- 9. Determine the axis of symmetry and the vertex (maximum or minimum) of a quadratic.
- 10. Sketch a quadratic from its key features (intercepts, vertex, direction of opening).
- 11. Convert between expanded, factorised and vertex forms of a quadratic.
Applications and Discriminant (Extended)
- 12. Solve optimisation problems modelled by a quadratic (e.g. maximum area, maximum profit, projectile motion).
- 13. Solve a system consisting of a linear and a quadratic equation algebraically.
- 14. Use the discriminant $b^2 - 4ac$ to determine the nature of the roots (two distinct, one repeated, none).
- 15. Solve quadratic inequalities using a sketch or sign-table.
Assessments
Quadratic equations end-of-unit test
Criterion A
60 min
Written test on solving quadratic equations by factorising, by completing the square, and by using the quadratic formula, with some applied word problems.
Review Pack
Open review hub
Fluency Pack A — 40 questions
Fluency Pack B — 40 questions
Problem-solving — 12 unfamiliar tasks
Worked solutions (Pack A + B + problems)