Answer:
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!