Answer:
- height: 71.33 feet
- reach: 82.10 feet
Step-by-step explanation:
The equation can be rewritten to vertex form:
 h(x) = -0.03(x² - 200/3x) +38
 h(x) = -0.03(x² -200/3x +(100/3)²) +38 +.03(100/3)²
 h(x) = -0.03(x -33 1/3)² +71 1/3
The vertex is (33 1/3, 71 1/3), so the maximum height the water will reach is 71 1/3 feet.
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When h(x) = 0, the water reaches as far as it possibly can.
 0 = -0.03(x -33 1/3)² +71 1/3
 (-71 1/3)/(-0.03) = (x -33 1/3)² . . . subtract 71 1/3; divide by -0.03
 √(2377.78) = x -33.33 . . . . . . . . positive square root
 82.10 ≈ x
The maximum distance the water will reach is 82.10 feet.
