Question 1198214
An arch is in the shape of a parabola.
 It has a span of 320 meters and a maximum height of 16 meters.
Find the equation of the parabola (assuming the origin is halfway between the arch's feet).
:
Using the form ax^2 + bx + c
Using the origin as the midpoint: c = 16 and x = -160 and + 160 when y = 0
x=-160, y = 0
-160^2a - 160b + 16= 0
and
x=+160, y = 0
160^2a + 160b + 16 = 0
:
25600a - 160b + 16 = 0
25600a + 160b + 16 = 0
--------------------------Adding eliminates b, find a
51200a + 0 + 32 = 0
simplify divide by 
1600a + 1 = 0
1600a = -1
a = -1/1600
a = -.000625
the equation
-.000625x^2 + 16 = 0
Looks like this
{{{ graph( 300, 200, -200, 200, -10, 20, -.000625x^2 + 16 ) }}}
:
Determine the height of the arch 90 meters from the center.
x = 90
y = -.000625(90^2) + 16
y = -5.0625 + 16
y = 10.9375 meters (green line
{{{ graph( 300, 200, -200, 200, -10, 20, -.000625x^2 + 16, 10.9375 ) }}}