The Lion's Gate Bridge in Vancouver , the Golden Gate Bridge in San Francisco , and the Brooklyn Bridge in New York City are examples of suspension bridges. A suspension bridge has 2 suspension cables that connect the tops of two towers. The roadway is suspended from these cables hence the name suspension bridge.

The height of a suspension cable above the roadway of a new suspension bridge , with two equally tall towers , is described by the equation y = 0.05(x-30)^2 + 6. In this equation , x represents the horizontal distance , in metres from one tower to the other tower , and y represents the height , in metres , of the cable above the roadway.

a) Complete the following table of values for the relationship ( alright I did A , what do I do for the others? Step by step please , thanks )

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Distance from First Tower , x (m) | Height of cable above roadway , y (m)

0 , 51

6 , 34.8

12, 22.2

18, 13.2

24, 7.8

30, 6

36, 7.8

42, 13.2

48, 22.2

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b) How high above the roadway is the suspension cable attached to the first tower?

c) Identify the coordinates of the vertex , the equation of the axis of axis of symmetry and the minimum value of the parabola.

e) How close to the roadway does the suspension cable dip? Justify your answer

f ) How far apart are the two towers? Explain how you deduced your answer

g) Vertical cables are used to join the suspension cable to the roadway. How long is the vertical cable that joins the suspension cable to the roadway at a point that is 6 m away from the first tower?

h) If vertical cables are required every 6m along the roadway , how much cable is needed for the entire bridge?