Find the coordinates of B .

Another point, C , which lies on the graph of \(y = f(x)\) has the same \(y\)-coordinate as A .
(i)     Plot and label C on the graph above.
(ii)    Find the \(x\)-coordinate of C .

\(x = - \frac{4}{{ - 2}}\)     (M1)
\(x = 2\)     (A1)

 OR

 \(\frac{{{\text{d}}y}}{{{\text{d}}x}} = 4 - 2x\)     (M1)
\(x = 2\)     (A1)
\((2{\text{, }}7)\) or \(x = 2\), \(y = 7\)     (A1)     (C3)

Notes: Award (M1)(A1)(A0) for 2, 7 without parentheses.

[3 marks]

(i)     C labelled in correct position on graph     (A1)     (C1)

(ii)    \(3 = 3 + 4x - {x^2}\)     (M1)

Note: Award (M1) for correct substitution of \(y = 3\) into quadratic.

\((x = )4\)     (A1)     (C2)

OR

Using symmetry of graph \(x = 2 + 2\) .     (M1)

Note: Follow through from their \(x\)-coordinate of the vertex.

\((x = )4\)     (A1)(ft)     (C2)

[3 marks]

In part b, the point C was sometimes not labelled or not shown on the graph provided. Candidates using their GDC to find the coordinates of the vertex needed to translate their calculator answer to the exact mathematical answer. Answers of \((1.9{\text{, }}7)\) or \((2.1{\text{, }}7)\) did not achieve the maximum number of marks. A common response in part c was to give \((4{\text{, }}3)\), with no working shown. This incurred a penalty of one mark. The correct answer to this question was \(x = 4\).

In part b, the point C was sometimes not labelled or not shown on the graph provided. Candidates using their GDC to find the coordinates of the vertex needed to translate their calculator answer to the exact mathematical answer. Answers of \((1.9{\text{, }}7)\) or \((2.1{\text{, }}7)\) did not achieve the maximum number of marks.