Answers

1. 1. The irrigation system is positioned 9.5 feet above the ground to start.
   2. The spray reaches a maximum height of 84.5 feet at a horizontal distance of 5 feet away from the sprinkler head.
   3. The spray reaches all the way to the ground at about 10.87 feet away​

   How to determine the position?

   Since the height (feet) of the spray of water is given by this equation h(x) = -x² + 10x + 9.5, we can logically deduce that the irrigation system is positioned 9.5 feet above the ground to start.

   How to determine the maximum height?

   For any quadratic equation with a parabolic curve, the axis of symmetry is given by:

   Xmax = -b/2a

   Xmax = -10/2(-1)

   Xmax = 5.

   Thus, the maximum height on the vertical axis is given by:

   h(x) = -x² + 10x + 9.5

   h(5) = -(5)² + 10(5) + 9.5

   h(5) = -25 + 50 + 9.5

   h(5) = 34.5 feet.

   Therefore, the spray reaches a maximum height of 84.5 feet at a horizontal distance of 5 feet away from the sprinkler head.

   Also, the spray reaches all the way to the ground at about:

   Maximum distance = √34.5 + 5

   Maximum distance = 10.87 feet.

   Read more on maximum height here: https://brainly.com/question/24288300

   #SPJ1

   Complete Question:

   An irrigation system (sprinkler) has a parabolic pattern. The height, in feet, of the spray of water is given by the equation h(x) = -x² + 10x + 9.5, where x is the number of feet away from the sprinkler head (along the ground) the spray is.

   1. The irrigation system is positioned____ feet above the ground to start.

   2. The spray reaches a maximum height of ____feet at a horizontal distance of feet away from the sprinkler head.

   3. The spray reaches all the way to the ground at about_____ feet away​

   Reply