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Algebra · Guided Practice

Completing the Square

12 questions with answers and video solutions. Try each one before revealing the answer.

1
Express x2+10x+28\displaystyle x^2+10x+28 in the form (x+p)2+q\displaystyle \left(x+p\right)^2+q
2
Express x2+6x+1\displaystyle x^2+6x+1 in the form (x+a)2+b\displaystyle \left(x+a\right)^2+b
3
Express x2−2x+5\displaystyle x^2-2x+5 in the form (x+m)2+n\displaystyle \left(x+m\right)^2+n
4
Express x2−4x−9\displaystyle x^2-4x-9 in the form (x+a)2+b\displaystyle \left(x+a\right)^2+b
5
Express x2+5x−1\displaystyle x^2+5x-1 in the form (x+p)2+q\displaystyle \left(x+p\right)^2+q
6
Express x2−9x+3\displaystyle x^2-9x+3 in the form (x+p)2+q\displaystyle \left(x+p\right)^2+q
7
Find the coordinates of the turning point of the graph of y=x2−8x+5.\displaystyle y=x^2-8x+5.
8
2014 P1 Q3
2 Marks

Express x2−14x+44\displaystyle x^2-14x+44 in the form (x−a)2+b\displaystyle \left(x-a\right)^2+b

9
2016 P2 Q9
2 Marks

Express x2+8x−7\displaystyle x^{2}+8x-7 in the form (x+a)2+b\displaystyle (x+a)^{2}+b.

10
2019 P2 Q10
2 Marks

Express x2+10x−15\displaystyle x^{2}+10x-15 in the form (x+p)2+q.\displaystyle (x+p)^{2}+q.

11
2022 P1 Q5
(2, 1)3 Marks

(a)  Express x2+8x+15\displaystyle x^{2}+8x+15 in the form (x+a)2+b\displaystyle (x+a)^{2}+b.

(b)  Hence, or otherwise, state the coordinates of the turning point of the graph of f(x)=x2+8x+15\displaystyle f(x)=x^{2}+8x+15.

12
2025 P2 Q5
2 Marks

Express x2+10x+19\displaystyle x^{2}+10x+19 in the form (x+a)2+b.\displaystyle (x+a)^{2}+b.

Practice questions courtesy of Maths.scot. Full written solutions are on his site — the links above go straight to them.

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