Question

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=-16x^(2)+194x+149

Answer 1

The maximum height reached by the rocket can be found by finding the vertex of the quadratic function. This occurs at the x-coordinate that is the average of the two x-intercepts. The maximum height reached by the rocket is approximately 498.6 feet to the nearest tenth of a foot.

Step-by-step explanation:

The maximum height reached by the rocket can be found by finding the vertex of the quadratic function. This occurs at the x-coordinate that is the average of the two x-intercepts. To find the x-coordinate of the vertex, use the formula x = -b / (2a), where a, b, and c are the coefficients of the quadratic equation. In this case, the equation is y = -16x^2 + 194x + 149, so a = -16, b = 194, and c = 149. Plugging in these values, we get x = -194 / (2 * -16) = 6.0625.

To find the maximum height, substitute the x-coordinate of the vertex back into the equation. Plugging in x = 6.0625, we get y = -16(6.0625)^2 + 194(6.0625) + 149 = 498.6 feet. Therefore, the maximum height reached by the rocket is approximately 498.6 feet to the nearest tenth of a foot.