Topics · Edexcel GCSE Maths (1MA1)

Completing the square

Higher only

Completing the square rewrites a quadratic so its turning point can be read straight off. Try it, then drag a curve to see why.

Exam-style questionNon-calculator3 marks

(a) Write $x^2 - 8x + 11$ in the form $(x + a)^2 + b$ , where $a$ and $b$ are integers.

(b) Hence write down the coordinates of the turning point of the graph of $y = x^2 - 8x + 11$

See why

Move the curve onto $y = x^2 - 8x + 11$ . Where is its turning point?

Your curve: $y = x^2$

Target: $y = x^2 - 8x + 11$ Your curve

Turning point x0Turning point y0

Drag the turning point, or use the sliders, until the curves match.

New contextNon-calculator3 marks

Find the coordinates of the turning point of the curve $y = x^2 + 6x + 2$

Completing the square and turning points

Short hands-on steps, then exam questions on this topic.

Specification A11 and A18 (Higher content): identify turning points by completing the square, and solve quadratics this way.
Higher tier only.
'Hence' in part (b) means use part (a): the turning point comes straight from the completed square.