Question 275891: The following function gives the height, (h) meters, of a batted baseball as a function of the time, t seconds, since the ball was hit.
h=-6(t-2.5)^2+38.5
How many seconds after it was hit did the ball hit the ground, to the nearest second?
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I have made an equation of 0=-6(t-2.5)^2+38.5 and then simplified it out to 0=-6t^2+30t+1 but don't know how to solve for t. i have looked at step by step calculators on a bunch of different sites but all of the instructions involved things that i have not learned yet. The answer in the back of the book is 5 and that's what all of the calculators say but i don't know how to get that answer. I just wanted to know if there is an easier way to solve this equation than the calculators give me. Thanks.
Answer by scott8148(6628)   (Show Source):
You can put this solution on YOUR website! start with the equation you made
subtracting 38.5 ___ -38.5 = -6(t - 2.5)^2
dividing by -6 ___ 6.417 = (t - 2.5)^2
taking square root ___ ±2.533 = t - 2.5 ___ remember square roots can be positive or negative
adding 2.5 ___ 5.033 = t ___ AND ___ -.033 = t
5 is the answer you are looking for
but the -.033 isn't just junk
___ it represents the time that the ball would have STARTED from the ground
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