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, 166, x, plus, 74
y=−16x
2
+166x+74
To find the maximum height reached by the rocket, we need to find the vertex of the parabolic function represented by the equation y = -16x^2 + 166x + 74.
The x-coordinate of the vertex of a parabola in the form y = ax^2 + bx + c is given by the formula x = -b/2a. In this case, a = -16 and b = 166.
x = -166/(2*(-16))
x = -166/(-32)
x = 5.1875
Now that we have found the x-coordinate of the vertex, we can find the y-coordinate by substituting this value back into the equation:
y = -16(5.1875)^2 + 166(5.1875) + 74
y ≈ -16(26.9) + 860 + 74
y ≈ -430.4 + 860 + 74
y ≈ 503.6
Therefore, the maximum height reached by the rocket is approximately 503.6 feet.