Final answer:
To find the maximum height of the firework, we calculate the time at which it is reached with the formula -b/2a, substitute into the height function, and determine the firework reaches a maximum height of 4 meters above sea level. The correct answer is option A.
Step-by-step explanation:
The question addresses the maximum height achieved by a malfunctioning firework according to its height function h(t) = -4.9t² + 29.4t - 40.1, where h represents the height in meters and t represents the time in seconds.
To find the maximum height, we need to calculate the vertex of the parabola represented by the quadratic function. This is done by using the formula -b/2a to find the time t at which the maximum height is reached, and then substituting this value back into the function h(t).
The vertex formula gives us the time
t_max = -b/(2a) = -29.4/(2 * -4.9) = 3 seconds.
Plugging this value into the height function, we get
h(3) = -4.9(3)² + 29.4(3) - 40.1
= -4.9 * 9 + 88.2 - 40.1
= -44.1 + 88.2 - 40.1
= 4 meters.
Therefore, the maximum height of the firework is 4 meters above sea level.