Final answer:
To find the x-coordinate at which the rocket will reach its maximum height, use the formula x = -b/2a. Plug in the values for a and b from the equation y = -16x^2 + 217x + 96 to find the x-coordinate.
Step-by-step explanation:
To find the x-coordinate at which the rocket will reach its maximum height, we can use the equation y = -16x^2 + 217x + 96, where y represents the height and x represents the time.
We can determine the maximum height by finding the vertex of the parabola. The x-coordinate of the vertex can be found using the formula x = -b/2a. For the given equation, a = -16 and b = 217. Plugging in these values, we get x = -217/(2*-16) = 6.78.
Therefore, the rocket will reach its maximum height at approximately x = 6.78.