Higher January 2022 Paper 1R Q20
20 The curve with equation \(y = \mathrm{f}(x)\) has one turning point.
The coordinates of this turning point are \((-6, -4)\)
(a) Write down the coordinates of the turning point on the curve with equation
(i) \(y = \mathrm{f}(x) + 5\)
(ii) \(y = \mathrm{f}(3x)\)
(2)The graph of \(y = \mathrm{g}(x)\) is shown on the grid below.

(b) On the grid, sketch the graph of \(y = 2\mathrm{g}(x)\) for \(-1 \leqslant x \leqslant 7\) (2)
The graph of \(y = \mathrm{h}(x)\) intersects the \(x\)-axis at two points.
The coordinates of the two points are \((-1, 0)\) and \((6, 0)\)
The graph of \(y = \mathrm{h}(x + a)\) passes through the point with coordinates \((2, 0)\), where \(a\) is a constant.
(c) Find the two possible values of \(a\) (2)
| Scheme | Marks |
|---|---|
| (i) Answer: \((-6, 1)\) | B1 |
| (ii) Answer: \((-2, -4)\) | B1 |
| (2) |
| Scheme | Marks |
|---|---|
| \((-1, 6)\), \((3, -2)\), \((7, 6)\) Answer: Fully correct graph | B2 |
| (2) |
Notes
B2: for a fully correct graph
(B1 for a V shape with least value at \((3, -2)\))
| Scheme | Marks |
|---|---|
| \(-3\), 4 | B2 |
| (2) | |
| (6 marks) |
Notes
B2: for 2 correct values in any order
(B1 for 1 correct value)