Question

Daniel dives into a swimming pool. The height of his head is represented by the function h(t) = -8t(squared) - 28t + 60, where t is the time in seconds and h(t) is the height of his head, in inches. How many seconds will it take for Daniel's head to reach the surface of the pool?

Answer 1

It should take him 1.5 sec to get to the top :)

Answer 2

When Daniel's head reaches the surface, h(t) = 0
Therefore:
-8t² - 28t + 60 = 0 To simplify, divide both sides by -4
2t² + 7t - 15 = 0
Consider the trinomial ax² + bx + c
To factor by grouping, we must find two numbers that multiply to equal AC (-30) and add up to B (7)
Two numbers that satisfy this are 10 and -3:
2t² + 10t - 3t - 15 = 0 Rewrite the equation using 10t and -3t
2t (t + 5) -3 (t +5) = 0 Regroup, then rewrite
(2t -3) (t+5) = 0

2t-3 = 0
2t = 3
t = 3/2
OR
t + 5 = 0
t = -5

We know t cannot be a negative number, so the answer is:
t = 3/2, or 1 and a half seconds