(a)     Express the quadratic $3{x^2} - 6x + 5$ in the form $a{(x + b)^2} + c$, where a, b, c $\in \mathbb{Z}$.

(b)     Describe a sequence of transformations that transforms the graph of $y = {x^2}$ to the graph of $y = 3{x^2} - 6x + 5$.

(a)     attempt at completing the square     (M1)

$3{x^2} - 6x + 5 = 3({x^2} - 2x) + 5 = 3{(x - 1)^2} - 1 + 5$     (A1)

$= 3{(x - 1)^2} + 2$     A1

$(a = 3,{\text{ }}b = - 1,{\text{ }}c = 2)$

(b)     definition of suitable basic transformations:

${{\text{T}}_1} =$ stretch in y direction scale factor 3     A1

${{\text{T}}_2} =$ translation $\left( {\begin{array}{*{20}{c}}   1 \\   0 \end{array}} \right)$     A1

${{\text{T}}_3} =$ translation $\left( {\begin{array}{*{20}{c}}   0 \\   2 \end{array}} \right)$     A1

[6 marks]

There were fewer correct solutions to this question than might be expected with a significant minority of candidates unable to complete the square successfully and a number of candidates unable to describe the transformations. A minority of candidates knew the correct terminology for the transformations and this potentially highlights the need for teachers to teach students appropriate terminology.