a rock is thrown from the top of a tall building. the distance, in feet, between the rock and the ground x seconds after it is thrown is given by f(x) =-16x^2-4x+382 How long after the rock is thrown is it 340 feet from the ground?

1.5 seconds

Step-by-step explanation:

Since f(x) represents the distance from the ground to the rock (in feet), we just need to find the values of x for which f(x) = 340. Substituting f(x) = 340 into f(x) = -16x² - 4x + 382 gives us:

340 = -16x² - 4x + 382

0 = -16x² - 4x + 42 (Subtract 340 from both sides)

16x² + 4x - 42 = 0  (Multiply entire equation by -1, "flip" equation)

8x² + 2x - 21 = 0    (Divide entire equation by 2)

(4x + 7)(2x - 3) = 0  (Factor LHS)

4x + 7 = 0 or 2x - 3 = 0 (Zero Product Property)

4x = -7 or 2x = 3 (Subtract -7 and add 3 from/to both sides, respectively)

or  

x = -1.75 is an extraneous solution because in the context of the question, you can't have negative seconds so therefore, the final answer is 1.5 seconds.

Hope this helps!