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, equals, minus, 16, x, squared, plus, 142, x, plus, 124
y=−16x
2
+142x+124

Answer 1

The maximum height reached by the rocket, described by the quadratic equation y = -16x² + 142x + 124, is approximately 439.0625 feet. This height is found by determining the vertex of the parabola, which is the point (x, y) where the maximum value of y is attained.

Step-by-step explanation:

To find the maximum height reached by the rocket, we must look at the provided quadratic equation for height as a function of time:
y = -16x² + 142x + 124. This equation is of the format ax² + bx + c, which represents a parabola. Since the coefficient of x² is negative, this parabola opens downwards, indicating that the vertex of the parabola is the maximum height reached by the rocket.

The x-coordinate of the vertex, which gives us the time at which the maximum height is achieved, is found using the formula -b/(2a). For our equation, a = -16 and b = 142, thus:

• x = -142/(2 * -16)
• x = 142/32
• x = 4.4375 seconds (approx)

To find the maximum height, we substitute this value back into the original equation:

• y = -16(4.4375)² + 142(4.4375) + 124
• y ≈ 439.0625 feet (to the nearest tenth)

Therefore, the maximum height reached by the rocket is approximately 439.0625feet.