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?
answers
h(-2), h(2), h(0)

Answer 1

To answer the questions based on the function \( h(t) = -16t^2 + 32t + 3 \):

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

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

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

Calculating this step by step:

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

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

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

The value \( h(1.74) \) represents the height of the baseball \( t \) seconds after it was hit, specifically at \( t = 1.74 \) seconds. In practical terms, this means that \( h(1.74) \) indicates how high the baseball is above the ground \( 1.74 \) seconds after Matt hit it.

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

Now let's analyze the given options: \( h(-2) \), \( h(2) \), and \( h(0) \).

- \( h(-2) \): This asks for the height of the baseball 2 seconds before it was hit, which is not valid in the context since time cannot be negative.
- \( h(0) \): This represents the height of the baseball at the moment it was hit (\( t = 0 \)).
- \( h(2) \): This refers to the height of the baseball at 2 seconds after it was hit, which is valid.

Thus, the value that would **not be valid** in the context of this problem is:

**\( h(-2) \)**.