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 the maximum height reached by the rocket, to the nearest tenth of a foot.
y, equals, minus, 16, x, squared, plus, 272, x, plus, 150
y=−16x
2
+272x+150
To find the maximum height reached by the rocket, we need to find the vertex of the parabolic equation. The equation of the vertex of the parabola y=ax^2+bx+c is given by x=-b/(2a).
In this case, a=-16 and b=272.
x = -272 / (2*-16) = -272 / -32 = 8.5
To find the maximum height, substitute x=8.5 back into the equation:
y = -16(8.5)^2 + 272(8.5) + 150
y = -16(72.25) + 2312 + 150
y = -1156 + 2312 + 150
y = 1306
Therefore, the maximum height reached by the rocket is 1306 feet.