Question

After 4 seconds, a launched projectile reaches a

maximum height of 60 feet. The projectile is launched
from a height of 12 feet.
If all the experiments that followed met or exceeded
this path, which quadratic inequality in standard form
contains the points in the later experiments?

Answer 1

The quadratic inequality that contains the points in the later experiments is -16a + 4b ≥ 48.

Step-by-step explanation:

To find the quadratic inequality that contains the points in the later experiments, we need to consider the maximum height reached by the projectile after 4 seconds.

Let's assume the projectile follows a parabolic path represented by the equation h(t) = -at^2 + bt + c, where h(t) is the height of the projectile at time t, a is the coefficient of the squared term, b is the coefficient of the linear term, and c is a constant.

In this case, the maximum height of 60 feet occurs at t = 4 seconds, so we can substitute these values into the equation to find a quadratic inequality.

We have h(4) = -a(4)^2 + b(4) + c = 60. Considering that the projectile is launched from a height of 12 feet, we can also substitute t = 0 into the equation to find h(0) = -a(0)^2 + b(0) + c = 12.

Combining these equations, we get -a(16) + 4b + c = 60 and c = 12.

Now, we can rewrite the equation as -16a + 4b = 48 and substitute c = 12 into it.

This gives us -16a + 4b = 48. Therefore, the quadratic inequality in a standard form that contains the points in the later experiments is -16a + 4b ≥ 48.