The main span of the Verrazzano-Narrows bridge in New York City has a central span that is about 1300m wide. The main cable supporting this span is about 150 m above the road at the top of each suspension tower and about 6 m above the road at its lowest point in the center. a. Show that the quadratic function to model the height (h) of the cable above the road in terms of the distance (d) from the left suspension tower is: ℎ = 0.000341
2 − 0.443 + 150, with the values of a and b shown to 3sf. [2 marks]
Note: You must show the unrounded values to earn full credit, along with the method used to obtain the quadratic function. Although you may use your GDC, this is NOT a question where using quadratic regression on your Stat menu will be sufficient to earn method marks, because you already have been given the answer. Your task is to show why the given model is the appropriate choice of a model.
b. Write down the domain and range, using interval notation. [2 marks]
c. Using your model, find the height of the cable at a point 100 m from the left tower support.
[2 marks]
d. At what distances from the left support tower is the cable less than 50 m above the road?
[3marks]