Topic summary · Pure foundations (P1)

Quadratics summary

Quadratics appear as equations, inequalities and graphs. Factorising, completing the square and the formula are the three standard routes.

Open Learning Sheet — Quadratics Download Quadratics answers PDF

Files: P1-Quadratics.pdf · P1-Quadratics answers.pdf · free public downloads · diagrams in the PDFs

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

(x-2)(x-3)=0\Rightarrow x=2\text{ or }3

Factor pairs.

Worked example 2 — Quadratic formula

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

Working

x=-1\pm\sqrt{6}

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

Worked example 3 — Completing the square

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

Working

(x+3)^2-4

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.

Open Learning Sheet Answers PDF

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