SOLUTION: The B Bridge connects SI and NY to NJ. It has an arch in the sharpe of a parabola that opens downward. Write an equation of a parabola to model the arch, assuming that the origin

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Question 271750: The B Bridge connects SI and NY to NJ. It has an arch in the sharpe of a parabola that opens downward. Write an equation of a parabola to model the arch, assuming that the origin is at the surface of the water, beneath the vertex of the arch. end to end bridge if 1675 ft; base to top is 325 ft.
This is in chapter 8, pg 424 problem 43 of Glencoe Mathematics, algebra 2
Answer by ankor@dixie-net.com(22740) (Show Source):
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The B Bridge connects SI and NY to NJ. It has an arch in the shape of a parabola that opens downward.
Write an equation of a parabola to model the arch, assuming that the origin is at the surface of the water,
beneath the vertex of the arch. end to end bridge if 1675 ft; base to top is 325
ft.
:
We can create a quadratic equation using the form: ax^2 + bx + c = y
c is 0, so we can just solve for a and b, using elimination:
:
x = 1675, y = 324 (the vertex)
1675^2a + 1675b = 325
2805625a + 1675b = 325
:
x = 3350, y = 0 (opposite end of the bridge where the arch at the water level)
3350^2a + 3350b = 0
11222500a + 3350b = 0
:
Multiply the 1st equation by 2, subtract the 2nd equation
561125a + 3350b = 650
11222500a + 3350b = 0
----------------------subtraction eliminates b, find a
-5611250a = 650
a =
a = -.0001158
:
Find b
-.0001158(1675^2) + 1675b = 325
-324.89 + 1675b = 325
1650b = 325 + 324.89
b =
b = .388
:
the equation of the arch y = -.0001158x^2 + .388x
:
A graph will illustrate this