A science class designed a container to protect an egg. Each prototype is launched from a machine at 9.4 meters per second from a roof 40 meters tall. The function f(t) = –4.9t2 + 9.4t + 40 represents the path from the building to the ground on the t-axis, where t is the amount of time since the launch.

The parabola opens downward, so its maximum height is at its vertex. The vertex occurs at t = −9.4 ÷ (2 × −4.9) ≈ 0.96 seconds, where the height is about 44.5 meters; mathematically, y ≤ 44.5. For the actual egg’s flight from launch until it reaches the ground, its height ranges from 40 meters up to 44.5 meters, then down to 0, so the reasonable range is 0 ≤ y ≤ 44.5. This matches choice C.

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