Question

The height h (in feet) of water spraying from a fire hose can be modeled by hx= -0.03x2+x+25, where x is the horizontal distance (in feet) from the fire truck. The crew lowers the ladder so that the water hits the ground 10 feet closer to the fire truck. Write a function that models the new path of the water.

Option 1: h(x) = -0.03x^2 + x + 15
Option 2: h(x) = -0.03x^2 + x + 35
Option 3: h(x) = -0.03x^2 + x + 20
Option 4: h(x) = -0.03x^2 + x + 10

Answer 1

The function that models the new path of the water, after the crew lowers the ladder and the water hits the ground 10 feet closer, is h(x) = -0.03x^2 + x + 15 and corresponds to Option 1.

Step-by-step explanation:

The height h (in feet) of water spraying from a fire hose can be modeled by hx = -0.03x2 + x + 25, where x is the horizontal distance (in feet) from the fire truck. If the crew lowers the ladder so that the water hits the ground 10 feet closer to the fire truck, we need to account for the change in the distance the water travels horizontally. Since the original function has a constant term which represents the initial height of the water from the ground, reducing the horizontal distance by 10 feet means the water will hit the ground with the same height minus 10 feet. Therefore, the function that models the new path of the water would subtract 10 from the original constant term, resulting in hx = -0.03x2 + x + 15. So, the correct option is Option 1: h(x) = -0.03x2 + x + 15.