Final answer:
To find the maximum height reached by the rocket, which is described by the quadratic equation y=-16x²+239x+143, we calculate the vertex of the parabola. The maximum height occurs when x = -b / (2a), resulting in y being the peak value of the function.
Step-by-step explanation:
The question relates to finding the maximum height of a rocket that has been launched from a tower, using the provided quadratic equation. The equation for the height of the rocket in feet (y) as a function of time after launch in seconds (x) is y=-16x²+239x+143. To find the maximum height, we look for the vertex of this quadratic function, which gives us the value of x when y is at its peak.
Since the equation is in the standard form of ax² + bx + c, we can find the time x at which the maximum height occurs by using the formula x = -b / (2a). Plugging in the values from our equation, we get x = -239 / (2 * -16), which calculates to x = 7.46875 seconds. Substituting this value back into the original equation gives us the maximum height y to the nearest tenth of a foot.