Question 856050
The parabolic arch in the concrete bridge in the figure must have a clearance of 50 feet above the water and span a distance of 200 feet.
 Find the equation of the parabola after inserting a coordinate system with the origin at the vertex of the parabola and the vertical axis (pointing upward) along the axis of the parabola.
:
from the description, the x intercepts are -100 and +100 and y intercept +50
Using the form ax^2 + bx + c = y, c = 50, b will cancel,
two equations for coordinates: x=100, y=0 and x=-100, y=0
100^2a + 100b + 50 = 0
-100^2a - 100 + 50 = 0
which is
10000a + 100b + 50 = 0
10000a - 100b + 50 = 0
----------------------- adding eliminates b, find a
20000a + 100 = 0
20000a = -100
a = -100/20000
a = -.005
the equation: y = -.005x^2 + 50, looks like this
{{{ graph( 300, 200, -125, 125, -10, 60, -.005x^2+50) }}}