O-LevelAdditional MathematicsQuadratic functions4037/11 · May/June 2023 · Q110 Marks

1 (a) Write 5x²-14x+8 in the form a(x+b)² +c, where a, b and c are constants to be found.

(a)Write 5x²-14x+8 in the form a(x+b)² +c, where a, b and c are constants to be found.[3]
(b)Hence write down the coordinates of the stationary point on the curve y = 5x²-14x+8.[2]
(c)On the axes below, sketch the graph of y = |5x²-14x+8|, stating the coordinates of the points where the graph meets the coordinate axes. [Figure 1.1][3]
(d)Write down the range of values of k for which the equation |5x²-14x+8|= k has 4 distinct roots.[2]

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Mark scheme

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

[3] B1 for 5(x+b)²
B1 for (x-7/5)²
B1 for -9/5
Alternative: (3) B1 for a=5
B1 for b = -14/10 oe
B1 for c = -18/10 oe
[2] FTB1 for each, follow through on their a and b from (a)
or SC1 if differentiation is used in their (a) or restarted in (b)
dy/dx = 10x-14=0 then (7/5, -9/5)
[3] B1 for the correct shape. Must have the parabola part of the curve with maximum in the first quadrant and cusps on the x-axis. Ignore labelling of their maximum point if incorrect coordinates
B1 for (4/5, 0) and (2, 0), must have a correct shape in the first quadrant.
B1 for (0, 8) must have a correct shape.
[2] B1FT follow through from 0 and their -b in part (a)

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