Question

The height of a stream of water from the nozzle of a fire hose is modeled by h(x) =-0.03x2+ 2x + 38 where h(x) is the height in feet, of the stream of water x feet from the fire truck. 1. What is the maximum height the water from this nozzle can reach? What is the maximum distance from the firetruck a firefighter can stand and still reach the fire?

Answer 1

• height: 71.33 feet
• reach: 82.10 feet

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.