Question

Ana dives into a pool off of a springboard high dive.
Her height (in meters above the water),
\[x\] seconds after diving, is modeled by
\[h(x)=-5(x+1)(x-3)\]
What is the height of Ana above the water at the time of diving?
meters

Answer 1

To find Ana's height above the water at the time of diving, we need to evaluate the function \( h(x) \) at \( x = 0 \), since \( x \) represents the time in seconds after diving.

The height function is given by:

\[
h(x) = -5(x+1)(x-3)
\]

Substituting \( x = 0 \) into the function:

\[
h(0) = -5(0+1)(0-3)
\]
\[
h(0) = -5(1)(-3)
\]
\[
h(0) = -5 \times 1 \times -3
\]
\[
h(0) = 15
\]

Therefore, the height of Ana above the water at the time of diving is

\[
\boxed{15} \text{ meters}.
\]