The diagram shows a fountain display under an escalator of a shopping mall on a cartesian plane.The base of an escalator is represented by a straight line which is defined by the

equation y=-x + 5. The fountain jet nozzle is positioned at the origin (0,0). The curves c1, c2 and c3 shows 3 possible paths of a fountain.

The design brief is as follows:

i) Each water jet must have a peak vertical height of at least 2m.

ii) Each water jet must be unique and cannot touch the escalator at any point.

The following assumptions must be made:

a) The fountain jet nozzle produces jet sprays which are perfectly shaped parabolas.

b) Air resistance is negligible.

c) There is no wind that would distort the paths of the water jets.

Your task is to design three fountain sprays by deriving algebraically the three equations that represent the paths of the jet sprays on the cartesian plane. Each equation should be presented in the form y=ax^2 +bx+c, where a,b and c are integers. Present the derivation clearly, with all reasons and deductions explicitly stated. You should include the following:

(i) Deduce the value of c and the range of values of a based on the position of the fountain jet nozzle.

(ii) Formulate an inequality in terms of a and b based on the requirement that each water jet must have a peak vertical height of at least 2m.

(iii) Formulate an inequality in terms of a and b based on the requirement that each water jet cannot touch the escalator.

(iv) Hence, find three possible equations that represent the path of these jet sprays.

I can't post the attachment of the diagram

but i know that c = 0.

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