The trajectory of a rocket is represented by the function h(t) = -3t2 + 24t + 36, where h is height in meters and t is time in seconds.
At what time does the rocket reach its maximum height?
You merely want the vertex of the typical parabola
for y = ax^2 + bx + c, the x of the vertex is -b/(2a)
so for yours, the t of the vertex is -24/(-6) = 4
the max height is reached after 4 seconds
To find the time when the rocket reaches its maximum height, we need to determine the vertex of the quadratic function h(t) = -3t^2 + 24t + 36.
The formula to find the x-coordinate of the vertex of a quadratic function in the form f(x) = ax^2 + bx + c is given by x = -b / (2a).
For our function h(t) = -3t^2 + 24t + 36, a = -3 and b = 24.
Substituting these values into the formula, we have:
t = -24 / (2 * -3)
t = -24 / (-6)
t = 4
Therefore, the rocket reaches its maximum height at t = 4 seconds.
To find the time at which the rocket reaches its maximum height, we need to determine the maximum value of the function h(t) = -3t^2 + 24t + 36. The maximum height is achieved at the vertex of the parabolic function, which occurs at the axis of symmetry.
The formula for the axis of symmetry of a parabola given in the form y = ax^2 + bx + c is given by x = -b / (2a). In our case, the given function is h(t) = -3t^2 + 24t + 36, where a = -3 and b = 24.
Using the formula for the axis of symmetry, we have:
t = -b / (2a) = -(24) / (2(-3))
t = -24 / -6
t = 4
Therefore, the rocket reaches its maximum height at t = 4 seconds.