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)+174x+84

Answer 1

To determine the maximum height of the rocket, we evaluate the vertex of the given quadratic equation representing the rocket's height over time. Using the vertex formula, we find the time at which the rocket reaches its peak, then plug this value back into the height equation to find the maximum height, rounded to the nearest tenth.

Step-by-step explanation:

To find the maximum height reached by a rocket using the equation y = -16x2 + 174x + 84, we must identify the time at which the maximum height occurs. This time corresponds to the vertex of the parabola represented by the equation, which we can find by using the formula x = -b / (2a) for a quadratic equation in standard form ax2 + bx + c.

For our equation, a = -16, b = 174, and c = 84. Plugging these values into the vertex formula gives us:
x = -174 / (2 * -16) = -174 / -32 = 5.4375 seconds.

Next, we substitute x = 5.4375 back into the original equation to find the maximum height:
y = -16 * (5.4375)2 + 174 * 5.4375 + 84.

Computing this gives us the maximum height to the nearest tenth of a foot (y, rounded).