Completing the Square (Edexcel IGCSE Maths): Exam Questions

Write $x^{2}+6x-7$ in the form $( x + a )^{2} + b$ where $a$ and $b$are integers.

Write $x^{2}+2x-8$ in the form $( x + m )^{2} + n$

where $m$ and $n$are integers.

Express $x^{2}--10x+40$ in the form $(x+a)^{2}+b$, where $a$ and $b$ are integers.

The equation of a curve is $y=(x+3)^{2}+5$

Circle the coordinates of the turning point.

Write $x^{2}-10x+22$ in the form $( x - a )^{2} - b$

Write $x^{2}-6x+11$ in the form $( x - a )^{2} + b$

Write x² + 8x + 3 in the form (x + a)² - b.

Write $x^{2}-10x+16$ in the form $( x + a )^{2} + b$

Write $x^{2}+10x+14$ in the form $( x + a )^{2} + b.$

$x^{2}+4x-9=(x+a)^{2}+b$

Find the value of $a$ and the value of $b$.

•  *$a$ = ............................................
  

$b$ = ............................................

The expression $x^{2}---8x+21$ can be written in the form $( x - a )^{2} + b$ for all values of $x$.

Find the value of $a$ and the value of $b$.

The equation of a curve is $y=f(x)$ where $f(x)=x^{2}---8x+21$ The diagram shows part of a sketch of the graph of $y=f(x)$.

The minimum point of the curve is $M$.

Write down the coordinates of $M$.

Given that $x^{2 } - 6 x + 1 = ( x - a )^{2 } - b$ for all values of $x$.

(i) Find the value of $a$ and the value of $b$.

(ii) Hence write down the coordinates of the turning point of the graph of $y=x^{2}-6x+1$.

Given that $a,b$ and $c$ are integers,

express $3x^{2}+12x+19$ in the form $a(x+b)^{2}+c$

Express $4x^{2}--8x+7$ in the form $a(x+b)^{2}+c$ where $a,b$ and $c$ are integers.

Write $3x^{2}-12x+7$ in the form $a(x+b)^{2}+c$

The line $L$ is the line of symmetry of the curve with equation $y=3x^{2}-12x+7$

Using your answer to part (a) or otherwise, write down an equation of $L$.

Express $x^{2}+6\sqrt{2}x--1$ in the form $(x+a)^{2}+b$

Show your working clearly.

The equation of a curve is$y=x^{2}+14x+52$

By completing the square, work out the coordinates of the turning point. You must show your working.

(i) Write $x^{2}+4x-16$ in the form $( x + a )^{2} - b$.

(ii) Solve the equation $x^{2}+4x-16=0$. Give your answers in surd form as simply as possible.

$x$ = ........... or $x$ = .......... [4]

$x^{2}-12x+a=(x+b)^{2}$

Find the value of $a$ and the value of $b$.

$a$ = ...............................................

$b$ = ...............................................

(i) Write $x^{2}+8x-9$ in the form $( x + k )^{2} + h$.

(ii) Use your answer to part (i) to solve the equation $x^{2}+8x-9=0$.

$x=$................... or $x=$................... [2]

Write $x^{2}-18x-27$ in the form $( x + k )^{2} + h$.

Use your answer to part (a) to solve the equation $x^{2}-18x-27=0.$

$x=$.................... or $x=$....................

The curve C has equation   $y=x^{2}-8x+10$

Using the axes below, sketch the curve C.

On your sketch show clearly

(i) the exact coordinates of any points of intersection of C with the coordinate axes,

(ii) the coordinates of the turning point.

Write $x^{2}+10x+14$ in the form $( x + a )^{2} + b.$

Sketch the graph of $y=x^{2}+10x+14$, indicating the coordinates of the turning point.

Express $3x^{2}--6x+5$ in the form $a(x--b)^{2}+c$

Write $2x^{2}+16x+35$ in the form $a ( x + b )^{2} + c$ where $a,b,$ and $c$ are integers.

Hence, or otherwise, write down the coordinates of the turning point of the graph of $y=2x^{2}+16x+35$

Express $7+12x--3x^{2}$ in the form $a+b(x+c)^{2}$ where $a,b$ and$c$are integers.

$C$ is the curve with equation$y=7+12x--3x^{2}$

The point $A$ is the maximum point on $C$

Use your answer to part (a) to write down the coordinates of $A$

Express $7-12x-2x^{2}$ in the form $a + b ( x + c )^{2}$ where $a$ , $b$ and $c$ are integers.

The function$f$ is such that $f(x)=5+6x--x^{2}$ for $x \text{less} - \text{than} or \text{slanted} \text{equal} to 3$

Express $5+6x--x^{2}$ in the form $p--(x--q)^{2}$ where $p$ and $q$ are constants.

Write $5+12x-2x^{2}$ in the form $a+b(x+c)^{2}$ where $a$ , $b$ and $c$ are integers.

Express $7--4x--x^{2}$ in the form $p--(x+q)^{2}$ where $p$ and $q$ are constants.

$2x^{2}-6x+5$ can be written in the form $a(x-b)^{2}+c$

where $a,b$ and$c$ are positive numbers. Work out the values of $a,b$ and $c$.

$\begin{array}{rcl} a = ................... \\ b = ................... \\ c = ................... \end{array}$

Find the turning point of $y=x^{2}+4x-3$ by completing the square.

( ...................... , .....................)