A rocket is propelled from the top of a building 30 meters tall so that its height in meters (t) seconds after it is launched is presented by the function: h(t)= -9.8t2 + 45t + 30.

1)

To find the maximum height reached by the rocket, we need to determine the vertex of the parabolic function h(t).

The vertex of a parabola in the form of h(t) = ax^2 + bx + c can be found using the formula: t = -b / (2a), where t represents time.

In this case, a = -9.8, b = 45, and c = 30.

Substituting the values into the formula, we get: t = -45 / (2 * (-9.8)).

Simplifying further, we have: t = -45 / (-19.6).

Calculating, t = 2.295.

So, the rocket reaches its maximum height after approximately 2.295 seconds.

To find the maximum height reached, we can substitute this value of t back into the function h(t).

h(t) = -9.8t^2 + 45t + 30

Substituting t = 2.295, we have:

h(2.295) = -9.8(2.295)^2 + 45(2.295) + 30.

Calculating this expression, we find that the maximum height reached by the rocket is approximately 86.82 meters.