NASA launches a rocket at t=0 seconds. Its height, in meters above sea-level, as a function of time is given by h(t)=-4.9t2+46t+241.

The height \( h(t) \) of the rocket is given by the quadratic function:

\[
h(t) = -4.9t^2 + 46t + 241
\]

### Key Features of the Function

1. **Vertex (Maximum Height)**: The vertex of the parabola represents the maximum height of the rocket. The time \( t \) at which this occurs can be found using the formula:

   \[
   t = -\frac{b}{2a}
   \]

   where \( a = -4.9 \) and \( b = 46 \).

2. **Time of Flight**: The rocket will rise until it reaches its maximum height and then fall back down. To find the total time of flight, we need to determine when \( h(t) = 0 \).

3. **Maximum Height**: Once we find \( t \) for the vertex, we can plug it back into \( h(t) \) to find the maximum height.

### Steps to Solve

1. **Find the vertex time**:
   \[
   t = -\frac{46}{2 \cdot -4.9} = \frac{46}{9.8} \approx 4.69 \text{ seconds}
   \]

2. **Calculate maximum height**:
   \[
   h(4.69) = -4.9(4.69)^2 + 46(4.69) + 241
   \]

3. **Find the time when the rocket hits the ground**:
   Set \( h(t) = 0 \) and solve the quadratic equation.

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NASA launches a rocket at t=0 seconds. Its height, in meters above sea-level, as a function of time is given by h(t)=-4.9t^2+46t+241.

Explore the calculation of a rocket's height as a function of time, represented by the quadratic equation h(t) = -4.9t^2 + 46t + 241. Learn how to find the maximum height and time of flight for a rocket launched by NASA.

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