Question

The path of a launched toy rocket can be modeled using a quadratic equation. Which of the models would be most helpful in finding the time it takes the rocket to reach the ground?

a) y = -16t(t - 5) + 1
b) y = -16t^2 - 52t + 3
c) y = -16(t + 2)(t - 8)
d) y = -(t - 3)^2 + 150

Answer 1

The most helpful model in finding the time it takes the rocket to reach the ground is option b) y = -16t^2 - 52t + 3.

Step-by-step explanation:

The most helpful model in finding the time it takes the rocket to reach the ground is option b) y = -16t^2 - 52t + 3.

To find the time, we need to find the roots of the quadratic equation, which represent the times when the rocket reaches the ground. In this equation, the coefficient of the t^2 term is -16, which represents the acceleration due to gravity. The positive root gives the time it takes for the rocket to reach the ground.

Using the quadratic formula, we can solve -16t^2 - 52t + 3 = 0 to find the time.