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) = -x^2+10x+7.5 where x is the number of feet away from the sprinkler head (along the ground) the spray is.

The irrigation system is positioned____ feet above the ground to start.
The spray reaches a maximum height of ____feet at a horizontal distance of feet away from the sprinkler head.
The spray reaches all the way to the ground at about_____ feet away​

Answer 1

7.5

32.5

5

maximum

10.7

Explanation:

Answer 2

9514 1404 393

Answer:

• 7.5 ft
• 32.5 ft, 5 ft
• 10.7 ft

Explanation:

a) The starting height is h(0) = 7.5 feet, the constant in the quadratic function.

The irrigation system is positioned 7.5 feet above the ground

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b) The axis of symmetry for quadratic ax^2 +bx +c is x = -b/(2a). For this quadratic, that is x=-10/(2(-1)) = 5. This is the horizontal distance to the point of maximum height. The maximum height is ...

h(5) = (-5 +10)(5) +7.5 = 32.5 . . . feet

The spray reaches a maximum height of 32.5 feet at a horizontal distance of 5 feet from the sprinkler head.

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c) The maximum distance will be √32.5 + 5 ≈ 10.7 ft.

The spray reaches the ground at about 10.7 feet away.