GCSE · Quadratic equations

Completing the squareExam-style questions

Why x² + bx is a square with a corner missing, why the bracket takes HALF of b, and how the completed form solves equations exactly and hands you the turning point for free.

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14 questions · GCSE (Higher) level · mark scheme and worked solution on each · no sign-up to try

DifficultyAll Level 3 Level 4 Level 5

1
Write $2x^2 + 12x + 5$ in the form $a(x + p)^2 + q$
Level 5 · 3 marksTry it
2
Show that $x^2 - 4x + 9$ is positive for all values of $x$ .
Level 5 · 3 marksTry it
3
Write $3x^2 - 12x + 5$ in the form $a(x + p)^2 + q$
Level 5 · 3 marksTry it
4
(a) Write $x^2 + 8x + 3$ in the form $(x + a)^2 + b$

(b) Write down the coordinates of the minimum point of the graph of $y = x^2 + 8x + 3$

(c) Explain why the equation $x^2 + 8x + 3 = -20$ has no solutions.
Level 5 · 4 marksTry it