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
(a) Write $x^2 + 8x + 3$ in the form $(x + a)^2 + b$ , where $a$ and $b$ are integers. (2 marks)
(b) Hence solve the equation $x^2 + 8x + 3 = 0$

Give your answers in surd form. (2 marks)
Level 4 · 4 marksTry it
2
Solve $x^2 + 6x - 5 = 0$ by completing the square.

Give your answers in the form $a \pm \sqrt{b}$ , where $a$ and $b$ are integers. [4]
Level 4 · 4 marksTry it
3
$M$ is the turning point of the curve with equation $y = 4x^2 - 20x + 9$

Find the coordinates of $M$ .

(3 marks)
Level 4 · 3 marksTry it
4
(a) Write $x^2 - 8x + 3$ in the form $(x - a)^2 - b$

(b) Hence write down the coordinates of the turning point of the graph of $y = x^2 - 8x + 3$
Level 4 · 3 marksTry it
5
Solve $x^2 + 10x + 18 = 0$ by completing the square.

Give your answers in surd form.
Level 4 · 4 marksTry it

2 more questions on completing the square

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