Higher January 2022 Paper 1R Q20

EdexcelHigherCurrent spec6 marksGraphical Transformations

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.

Grid with x from -4 to 8 and y from -4 to 6 showing a V-shaped graph y = g(x) through (-4, 6), (0, 2), (2, 0), minimum point (3, -1), (4, 0) and (8, 4)
(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)
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