Quadratics summary

Key learning points

• Factorise when integer roots look likely; otherwise complete the square or use the formula.
• Discriminant $b^2-4ac$ counts real roots.
• Vertex from completing the square or $x=-\frac{b}{2a}$.
• Sketch using the sign of $a$ and the intercepts.

Worked example 1 — Factorise and solve

Solve $x^2-5x+6=0$.

Working

Factor pairs.

Worked example 2 — Quadratic formula

Solve $x^2+2x-5=0$ in surd form.

Working

$x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}$.

Worked example 3 — Completing the square

Write $x^2+6x+5$ in completed-square form.

Working

Half of 6 is 3.

Scaffolded Learning Sheet and answers (PDFs)

This page is a short, searchable overview for revision and search engines. Use the Scaffolded Learning Sheet first, then the Answers PDF for a full written solution. The printable PDFs remain the main classroom resource.