Question 1

Paper 2Medium6 marks

An engineer models the height hh in metres, of the lower edge of an arch above a level path by

h(x)=ax2+bx+c,h(x)=ax^2+bx+c,

where xx is the horizontal distance, in metres, from a marker. The model is assumed to pass exactly through the observations below.

xx024
h(x)h(x)1.104.104.30
(a)

Write down a system of linear equations in aa bb and cc from these observations.

[2]
(b)

Using your system from part (a), use a GDC to solve it and hence show that

h(x)=−0.35x2+2.20x+1.10.h(x)=-0.35x^2+2.20x+1.10.
[2]
(c)

The arch meets the path when h(x)=0h(x)=0 Use the model to determine the positive value of xx to three significant figures, and state what it represents.

[2]

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