Answer:
t ∈ {0.209, 4.791}
Step-by-step explanation:
Substituting 8 for h, we want to find t using ...
... 8 = 3 +25t -5t^2
... 5t^2 -25t +5 = 0 . . . . . subtract the right side to get standard form
... t^2 -5t +1 = 0 . . . . . . . . divide by 5 (makes the leading coefficient 1)
... (t -2.5)^2 -5.25 = 0 . . . rewrite to vertex form*
... t = 2.5 ± √5.25 . . . . . . add 5.25, square root, add 2.5
Rounded to milliseconds, the times are 209 ms and 4.791 s.
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* The vertex of this function is different from that of the graph because we have shifted it down 8, and removed a vertical scale factor of -5 relative to the one that is graphed.
