(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.