how far across the river does the water land?

Question

on one of the banks f the chicago river, there is a water cannon, called the water arc, that sprays recirculated water across the rivr. the path of the water arc is given by the model y=0.006x^2+1.2+10 where x is the distance (in feet) across the river and y is the height f the arc (in feet)

Answer 1

The water arc takes a parabolic path. We can find where this path ends by simply finding where y=0, because that is when the height of the water is 0, meaning the water has touched the ground.

It appears you made a typo in writing the problem out, so I assume the actual arc is

y = -.006x^2 + 1.2x + 10

Using the quadratic equation with a= -.006, b = 1.2, c = 10, we get:

x = (-1.2 + sqrt(1.2^2 - 4*.006*10))/(2*-.006)

-> x = ~208 feet