A rocket is launched from a tower. The height of the rocket, y in feet, is related to the time after launch, x in seconds, by the given equation. Using this equation, find out the time at which the rocket will reach its max, to the nearest 100th of a second.
y, equals, minus, 16, x, squared, plus, 163, x, plus, 138
y=−16x
2
+163x+138
To find the time at which the rocket will reach its maximum height, we need to find the vertex of the parabolic equation y = -16x^2 + 163x + 138.
The x-coordinate of the vertex is given by the formula x = -b / 2a, where a = -16 and b = 163.
Plugging in the values, we get:
x = -163 / (2 * -16)
x = -163 / -32
x = 5.09 (rounded to the nearest hundredth)
Therefore, the rocket will reach its maximum height at approximately 5.09 seconds after launch.