The equation given for the height of the rocket above the ground is:
h(t) = -2.24(t - 6)^2 + 126
Where:
- t is the time in seconds since the rocket was launched.
- h(t) is the height of the rocket above the ground in feet.
This equation represents a quadratic function in vertex form, where the vertex is the highest point reached by the rocket.
The vertex of the quadratic function h(t) = a(t - h)^2 + k is given by the point (h, k). In this case, the vertex is (6, 126), meaning the rocket reaches its maximum height at t = 6 seconds, and the maximum height attained is 126 feet.
The coefficient a = -2.24 indicates that the parabola opens downwards, reflecting the fact that the rocket goes up and then comes down.
So, Mr. Zika's rocket reached its maximum height of 126 feet 6 seconds after launch and then descended back to the ground.
