Question

At baseball practice, Matt hit the ball into the outfield. The function h(t)=−16t2+32t+3
gives the height h(t)
of the baseball in feet, t
seconds after it is hit.

A) What is the value of h(1)
? Response area

B) What does h(1.74)
represent in context? Response area

C) Which value would not be valid in the context of this problem? Response area

Answer 1

Let's analyze the function \( h(t) = -16t^2 + 32t + 3 \) step by step for each part of the question.

### A) What is the value of \( h(1) \)?

To find \( h(1) \), substitute \( t = 1 \) into the function:

\[
h(1) = -16(1)^2 + 32(1) + 3
\]
\[
= -16(1) + 32 + 3
\]
\[
= -16 + 32 + 3
\]
\[
= 16 + 3 = 19
\]

So, the value of \( h(1) \) is **19** feet.

### B) What does \( h(1.74) \) represent in context?

In the context of this problem, \( h(1.74) \) represents the height of the baseball after it has been hit for approximately 1.74 seconds. Specifically, it tells us how high above the ground the baseball is at that particular moment in time.

### C) Which value would not be valid in the context of this problem?

In the context of this problem, time \( t \) represents the number of seconds after the baseball is hit. As time cannot be negative in this scenario:

- A negative value of \( t \) would not be valid. Thus, any \( t < 0 \) (e.g., \( t = -1 \)) would not make sense in this context, since you cannot have negative time before the baseball is hit.

Therefore, any negative value for \( t \) would not be valid.