The diagram below shows the gate of an art gallery. A concrete structure is built at the upper part of the gate and the words 'ART GALLERY' is written on it. The top of the concrete structure is flat whereas the bottom is parabolic in shape. The concrete structure is supported by two vertical pillars at both ends.

The distance between the two pillars is 4 metres and the height of the pillar is 5 metres. The height of the concrete structure is 1 metre. The shortest distance from point A of the concrete structure to point B, that is the highest point on the parabolic shape, is 0.5 metres.



(a) The parabolic shape of the concrete structure can be represented by various functions depending on the point of reference. Based on different points of reference, obtain at least three different functions which can be used to represent the curve of this concrete structure.
(b) The front surface of this concrete structure will be painted before the words 'ART GALLERY' is written on it. Find the area to be painted.

FURTHER EXPLORATION
(a) You are given four different shapes of concrete structures as shown in the diagrams below. All the structures have the same thickness of 40 cm and are symmetrical.






(i) Given that the cost to construct t cubic metre of concrete is RM840.00, determine which structure will cost the minimum to construct.
(ii) As the president of the Arts Club, you are given the opportunity to decide on the shape of the gate to be constructed. Which shape would you choose? Explain and elaborate on your reasons for choosing the shape.

(p) The following questions refer to the concrete structure in the diagram below. If the value of k increases with a common difference of 0.25 m;
(i) complete Table 1 by finding the values of k and the corresponding areas of the concrete structure to be painted.
(ii) observe the values of the area to be painted from Table 1. Do you see any pattern? Discuss.





(c) Express the area of the concrete structure to be painted in terms of k. Find the area a k approaches the value of 4 and predict the shape of the concrete structure.

REFLECTION
While you were conducting the project, what have you learnt? What moral values did you practise? Represent your opinions or feelings creatively through usage of symbols, illustrations, drawings or even in song.

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