Final answer:
The maximum height of the model rocket can be found by solving for the vertex of the given quadratic function. The vertex is (6, 224) and the maximum height is 224 feet.
Step-by-step explanation:
The function y = -16x^2 + 192x +2 represents the height y (in feet) of a model rocket x seconds after it is launched. The highest point in any trajectory is reached when vy = 0. By substituting the given equation into the equation v² = v² — 2g(y — yo), we can find the maximum height, y.
First, let's find the vertex of the given quadratic function. The x-coordinate of the vertex can be found using the formula -b/2a. For the equation y = -16x^2 + 192x +2, the x-coordinate of the vertex is x = -192/(2*-16) = 6.
Substituting x = 6 into the equation, we can find the y-coordinate of the vertex. y = -16(6)^2 + 192(6) + 2 = 224.
Therefore, the vertex is (6, 224). The model rocket reaches a maximum height of 224 feet.