Question

The function
f
(
t
)
=
−
4.9
t
2
+
29.4
t
+
78.4
represents the height of a toy rocket,
f
(
t
)
, in meters
t
seconds after being launched from the top of a building.



Which equation shows when the rocket will land on the ground?



A.
f
(
t
)
=
−
4.9
(
t
−
2
)
(
t
+
8
)

B.
f
(
t
)
=
−
4.9
(
t
−
8
)
(
t
+
2
)

C.
f
(
t
)
=
−
4.9
(
t
−
3
)
2
+
87.4

D.
f
(
t
)
=
−
4.9
(
t
−
3
)
2
+
122.5

Answer 1

Set f(t) = 0 to find when the rocket hits the ground. Factor:

-4.9t^2 + 29.4t + 78.4 = -4.9(t - 8)(t + 2).

So f(t) = -4.9(t - 8)(t + 2), which is choice B. The physically relevant root is t = 8 seconds.