We know the equation of a parabola can be written as
y = a(x-b1) (x-b2) where a is a constant and b1 and b2 are the zeros
y = a ( x - 48) ( x - -48)
y = a ( x-48) (x+48)
Now when x = 0 y = 8
8 = a ( 0-48) ( 0+48)
8 = a (-2304)
-8/2304 = a
-1/288 = a
y = -1/288 ( x-48) (x+48)
This is the equation for the parabola
Now let y = 2
2 = -1/288 ( x-48) (x+48)
Multiply each side by -288
-576 = (x-48)(x+48)
FOIL
-576 = x^2- 2304
ADD 2304 to each side
1728=x^2
Take the square root of each side
24 sqrt(3) = x
24 sqrt(3) ft
41.569 ft
