Final answer:
The time when the rocket is at its highest point is 4.25 seconds.
Step-by-step explanation:
To find the time when the rocket is at its highest point, we need to determine the vertex of the quadratic equation. The equation for the height of the rocket is h = -16t² + 136t + 72. The vertex of a quadratic equation of the form y = ax² + bx + c is given by the formula t = -b/2a. Plugging in the values from our equation, we get t = -136/(2*-16) = 4.25 seconds. So, when the rocket is at its highest point, 4.25 seconds have gone by.