Question

a diver stands at the end of a diving board and jumps off into the water. The path of the diver is modeled by the function h(x)= -(x-2)2 + 9, where h(x) is the height above the water in feet, and x is time in seconds. Determine the new function that models the diver's jump after the following changes. The diving board is extended by 0.5 feet

Answer 1

To model the diver's jump after the diving board is extended by 0.5 feet, we need to adjust the function \( h(x) = -(x - 2)^2 + 9 \).

1. **Understand the original function:**
The original function indicates that the diver reaches a maximum height of 9 feet at \( x = 2 \) seconds. The vertex form of the function shows that the height above the water depends on time.

2. **Change in height due to extended board:**
Extending the diving board by 0.5 feet means that the maximum height is increased by 0.5 feet. Therefore, the new maximum height will be \( 9 + 0.5 = 9.5 \) feet.

3. **Rewriting the function with the new maximum height:**
Since the extension does not affect the time at which the diver reaches the maximum height (which remains at \( x = 2 \)), we only need to update the height in the equation:
\[
h(x) = -(x - 2)^2 + 9.5.
\]

Thus, the new function that models the diver's jump after the diving board has been extended by 0.5 feet is:
\[
h(x) = -(x - 2)^2 + 9.5.
\]