Question 271750
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 = {{{650/(-5611250)}}}
a = -.0001158
:
Find b
-.0001158(1675^2) + 1675b = 325
-324.89 + 1675b = 325
1650b = 325 + 324.89
b = {{{649.89/1675}}}
b = .388
:
the equation of the arch y = -.0001158x^2 + .388x
:
A graph will illustrate this
{{{ graph( 300, 200, -1000, 4000, -100, 400, -.00011158x^2+.388x) }}}