Edexcel IGCSE Math A 2.2.HD completing the square

Practise completing-square questions by rewriting quadratics as a(x-b)²+c and using the form to read a minimum or maximum point.

Exam points

Rewrite quadratics in completed-square form, including coefficients such as 5x².
Use a(x-b)²+c to identify a minimum or maximum point and its coordinates.
Factor out a negative or non-unit coefficient before completing the square.

[Maximum number: 2]

The graph of $y=\sin x^{\circ}$ for $0 \leqslant x \leqslant 360$ is drawn on the grid.

Figure for Question 2.2.HD Completing the square question 1 — Edexcel IGCSE Math A Higher

Write $x^{2}-6 x+10$ in the form $(x-a)^{2}+b$ where a and b are integers.

$(x-3)^2+1$

Marking guidance:
- B2 for $(x-3)^2+1$
- If not B2, award B1 for $\left(x-\frac{6}{2}\right)^2+n$ , where $n\ne1$ , or $(x-m)^2+1$ , where $m\ne3$ , or a valid completing-square expansion with 2a=6 or $a^2+b=10$

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2.2.HD Completing the square question 1