what is the maximum height f the water sprayed from the water arc?

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

You function needs to be      y = -0.006x² + 1.2x + 10.  This indicates a parabola opening downward.  This is the only type of parabola that has a maximum point.  So, now that I fixed your equation, lets find the maximum height.

 

 

To find the maximum height, we need to find the distance across the river in which the maximum height occurs.  We can find that by using the formula

 

x = -b/2a

 

where:

a = -0.006

b = 1.2

 

 

x = -1.2 / (2 *-0.006)

x = -1.2 * 0.012 

x = 100

 

This means that the maximum height occurs when the water is sprayed 100 feet across the river.

 

Now evaluate y when x=100.  This is the maximum height of the water

 

 

y = -0.006(100)² + 1.2x + 10

 

 

Finish up here.