A stone is thrown skyward from the top of building. The distance in feet between the stone and the ground in 't' seconds is given by the function h (t) = -16t(t) -4t+ 442. How long after the stone is thrown is it 430 feet from the ground?

Sorry I don't know how to type t squared.

just solve

-16t^2 + 4t + 442 = 430

Your equation, with -4t, has the stone being thrown downward. It seems to be at odds with the skyward initial toss.

No problem, I understand what you mean by "t squared". To solve for the time when the stone is 430 feet from the ground, we need to set the height function equal to 430 and solve for t.

The height function is given by h(t) = -16t^2 - 4t + 442, where t represents time in seconds and h(t) represents the height of the stone at time t.

To find the time when the stone is 430 feet from the ground, we set h(t) = 430:

-16t^2 - 4t + 442 = 430

Simplifying the equation, we get:

-16t^2 - 4t + 12 = 0

To solve this quadratic equation, we can use the quadratic formula:

t = (-b ± √(b^2 - 4ac)) / (2a)

In this case, a = -16, b = -4, and c = 12. Substituting these values into the formula, we get:

t = (-(-4) ± √((-4)^2 - 4(-16)(12))) / (2(-16))

Simplifying further:

t = (4 ± √(16 + 768)) / (-32)

t = (4 ± √784) / (-32)

t = (4 ± 28) / (-32)

This gives us two possible values for t:

t1 = (4 + 28) / (-32) = 32 / (-32) = -1

t2 = (4 - 28) / (-32) = -24 / (-32) = 0.75

Since time cannot be negative in this context, the only valid solution is t = 0.75. Therefore, the stone is 430 feet from the ground 0.75 seconds after it is thrown.