A baseball is thrown into the air from the top of a 224-foot tall building. The baseball's approximate height over time can be represented by the quadratic equation h(t) = -16t2 + 80t + 224, where t represents the time in seconds that the baseball has been in the air and h(t) represents the baseball's height in feet. When factored, this equation is h(t) = -16(t - 7)(t + 2). What is a reasonable time for it to take the baseball to land on the ground?

A.
7 seconds
B.
5 seconds
C.
2 seconds
D.
9 seconds

C.  2 seconds

Step-by-step explanation:

given equation:  h(t) = -16(t - 7)(t + 2).

A h(7) = -16(7 - 7)(7 + 2) = 0 second

B h(5) = -16(5 - 7)(5 + 2) = -336 seconds

C h(2) = -16(2 - 7)(2 + 2) = 320 seconds

D h(9) = -16(9 - 7)(9 + 2) = -352 seconds

therefore, the only reasonable time for the ball the reach the ground is 320 seconds,

so the answer is C.  2 seconds

δabc ≅ δdcb by sas because

db ≅ ac . . given (side)

bc ≅ bc . . reflexive property (side)

∠dbc ≅ ∠ acb . . alternate interior angles where transversal bc crosses parallel lines bd and ac (included angle)