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Answer:
The rocket will take 4.5 seconds to reach its maximum height.
Step-by-step explanation:
The height of a missile t seconds after it has been fired is given by h=-4.9*t²+44.1*t
This function is a quadratic function of the form f (x) = a*x² + b*x + c. In this case a=-4.9, b=44.1 and c=0
To calculate how many seconds it will take for the rocket to reach its maximum height, I must calculate the maximum of the function. The maximum of a quadratic function is the vertex of the parabola. The x coordinate of the vertex will be simply: . The y coordinate of the vertex corresponds to the function evaluated at that point.
In this case the x coordinate of the vertex corresponds to the t coordinate. In other words, by calculating the x coordinate of the vertex, you are calculating the maximum time t it will take for the rocket to reach its maximum height. So:
t=4.5
<u><em>The rocket will take 4.5 seconds to reach its maximum height.</em></u>