A-LevelMathematicsFunctions9709/12 · Oct/Nov 2023 · Q68 Marks

The equation of a curve is y = x² – 8x + 5.

(a)Find the coordinates of the minimum point of the curve.[2]
(b)The curve is stretched by a factor of 2 parallel to the y-axis and then translated by (1/4). Find the coordinates of the minimum point of the transformed curve.[2]
(c)Find the equation of the transformed curve. Give the answer in the form y = ax² + bx + c, where a, b and c are integers to be found.[4]

Mark scheme

Marking points from the official mark scheme (Oct/Nov 2023). The mark or mark type is shown in brackets.

[M1] Correct differentiation of x² and equating their dy/dx to 0.
[A1]
[B1 FT] Can be from finding the equation of the transformed curve, differentiating and putting dy/dx = 0.
[B1 FT] Can be from putting x = 8 in the equation of the transformed curve.
[B1] Can be implied if both transformations done together: 2((x-4)²-8(x-4)+5)+1 OE.
[M1] For the x translation, each x becomes (x-4).
[M1] For the y translation of +1.
[A1] Evidence to support their answer may be in (b) but answer must be seen in (c).

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