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 out the time at which the rocket will reach its max, to the nearest 100th of a second.

y, equals, minus, 16, x, squared, plus, 145, x, plus, 122
y=−16x
2
+145x+122

Answer 1

The rocket reaches its maximum height approximately 4.53 seconds after launch by using the vertex formula -b/(2a) on the quadratic equation y = -16x² + 145x + 122.

Step-by-step explanation:

The student's question relates to finding the time at which the rocket reaches its maximum height based on the given quadratic equation y = -16x² + 145x + 122. To identify this time, we use the formula for the vertex of a parabola represented by an equation in the form of ax² + bx + c. The vertex formula, which gives the x-coordinate of the vertex (the time in seconds when the height is maximum in this scenario), is -b/(2a). Here, a is -16, and b is 145.

Applying the vertex formula, we get:
x = -145 / (2 * -16) = 145 / 32 ≈ 4.53 seconds.

Therefore, the rocket reaches its maximum height approximately 4.53 seconds after launch.