Question

The height (in feet) of water spraying from a garden hose can be modeled by h(x) = -0.12 + 0.84x + 2.16, where x is the horizontal distance (in feet) from the opening of the hose. The hose is raised so that the water hits the ground 1 foot farther away. Write a function that models the new path of the water.

Answer 1

The new function that models the path of the water with the hose raised so it hits the ground 1 foot farther away is h(x) = -0.12(x-1)² + 0.84(x-1) + 2.16.

Step-by-step explanation:

The original function that models the path of the water is h(x) = -0.12x² + 0.84x + 2.16, where x is the horizontal distance from the opening of the hose. Now, the hose is raised so that the water hits the ground 1 foot farther away. This shift will result in a new function that is horizontally translated 1 unit to the right. The new function will be h(x) = -0.12(x-1)² + 0.84(x-1) + 2.16.

This represents a shift in the parabola to the right by 1 unit, which would model the new path of the water spraying from the hose. In practical terms, this means the water will hit the ground 1 foot farther away from the hose's opening.

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