Algebra · Guided Practice

Completing the Square

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

Express

\displaystyle x^2+10x+28

in the form

\displaystyle \left(x+p\right)^2+q

No hints on this one — its full written solution is with the answer.

Express

\displaystyle x^2+6x+1

in the form

\displaystyle \left(x+a\right)^2+b

No hints on this one — its full written solution is with the answer.

Express

\displaystyle x^2-2x+5

in the form

\displaystyle \left(x+m\right)^2+n

No hints on this one — its full written solution is with the answer.

Express

\displaystyle x^2-4x-9

in the form

\displaystyle \left(x+a\right)^2+b

No hints on this one — its full written solution is with the answer.

Express

\displaystyle x^2+5x-1

in the form

\displaystyle \left(x+p\right)^2+q

No hints on this one — its full written solution is with the answer.

Express

\displaystyle x^2-9x+3

in the form

\displaystyle \left(x+p\right)^2+q

No hints on this one — its full written solution is with the answer.

Find the coordinates of the turning point of the graph of

\displaystyle y=x^2-8x+5.

No hints on this one — its full written solution is with the answer.

2014 P1 Q3

2 Marks

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

2016 P2 Q9

2 Marks

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

2019 P2 Q10

2 Marks

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

2022 P1 Q5

(2, 1)3 Marks

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

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

2025 P2 Q5

2 Marks

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

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Completing the Square

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