Today's lesson · 29 October 2026
The quadratic formula and completing the square
Solving any quadratic exactly, reading the discriminant, and finding a turning point from completed-square form
Today's lesson is The quadratic formula and completing the square, a UK Year 11 (Key Stage 4 / GCSE HIGHER tier, ages 15 to 16) Math unit. Rotates every day, so check back tomorrow for a different unit.
Factorising is a lock-pick that only fits some doors. These two methods open every quadratic.
By Year 11 you can factorise x² - 5x + 6 into (x - 2)(x - 3) in seconds. But try x² - 5x + 3. No pair of whole numbers multiplies to 3 and adds to -5, so factorising simply cannot start. The equation still has two perfectly real solutions; they just happen to be irrational numbers involving .
What students will be able to do
Students will solve quadratic equations exactly by completing the square and by the quadratic formula (rearranging into standard form first where necessary), simplify surd answers fully, use the discriminant to state the number of real roots without solving, and find the turning point of a quadratic curve from its completed-square form.
Curriculum anchor
Teach the whole lesson
This is a short preview. Open the full teaching unit for the step-by-step teaching sequence, worked examples, misconceptions to watch for, guided practice, differentiation and an exit ticket, ready to deliver in class today.
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