A quarterback is standing at the top of the bleachers, trying to throw the football as high into the air as he can. He picks up the football so that it is 47 feet above the ground and throws the football as high as he can. The height of the football after t seconds can be modeled by the expression −16t^2 + 32t + 47. What does 47 represent in the context of the problem?

Question

A quarterback is standing at the top of the bleachers, trying to throw the football as high into the air as he can. He picks up the football so that it is 47 feet above the ground and throws the football as high as he can. The height of the football after t seconds can be modeled by the expression −16t^2 + 32t + 47. What does 47 represent in the context of the problem?
A) 47 represents the number of footballs they have at practice at a given time.
B) 47 represents the height of the football when the quarterback throws it.
C) 47 represents the number of seconds the quarterback holds the football before throwing it.
D) 47 does not make sense as a value in this problem.

GPT-4o mini · Answer

The expression given for the height of the football after \( t \) seconds is \( -16t^2 + 32t + 47 \). In this expression, the constant term \( 47 \) represents the height of the football at the moment it is thrown.

Therefore, the correct answer is:

B) 47 represents the height of the football when the quarterback throws it.