- The irrigation system is positioned 9.5 feet above the ground to start.
- The spray reaches a maximum height of <u>84.5 feet</u> at a horizontal distance of <u>5 feet</u> away from the sprinkler head.
- The spray reaches all the way to the ground at about 10.87 feet away
<h3>How to determine the position?</h3>
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.
<h3>How to determine the
maximum height?</h3>
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 <u>84.5 feet</u> at a horizontal distance of <u>5 feet</u> 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: brainly.com/question/24288300
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<u>Complete Question:</u>
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
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