Question

21. Water that is sprayed upward from a

sprinkler with an initial velocity of
20 m/s can be approximated by the
function y=-5x² + 20x, where y is
the height of a drop of water x seconds
after it is released. Graph this function.
Find the time it takes a drop of water
to reach its maximum height, the
water's maximum height, and the time
it takes the water to reach the ground.

Answer 1

• 2 seconds to maximum height
• 20 meters maximum height
• 4 seconds to reach the ground

Explanation:

The function can be graphed using a graphing calculator, geometry app, or spreadsheet. One such graph is attached. Often, these tools are capable of identifying extrema and intercepts.

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extreme

The vertex of the graph is reported as (x, y) = (2, 20). This means the maximum height is reached after 2 seconds. That maximum height is 20 meters.

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intercept

The drop is launched from ground level at x = 0 seconds. It returns to ground level at x = 4 seconds.