Question

Ana dives into a pool off of a springboard high dive. Her height (in meters above the water), x xx seconds after diving, is modeled by h ( x ) = − 5 ( x + 1 ) ( x − 3 ) h(x)=−5(x+1)(x−3)h, left parenthesis, x, right parenthesis, equals, minus, 5, left parenthesis, x, plus, 1, right parenthesis, left parenthesis, x, minus, 3, right parenthesis How many seconds after diving will Ana hit the water?

Answer 1

Answer: Ana will hit the water after 3 seconds.

Step-by-step explanation:

The exercise gives you the following function which models Anna's height  above the water (in meters) after diving "x" seconds:

$h(x)=-5(x+1)(x-3)$

You can rewrite the function with $h(x)=y$:

$y=-5(x+1)(x-3)$

In order to calculate the number of seconds Ana will hit the water after diving, the procedure is:

- Substitute $y=0$ into the function:

 $0=-5(x+1)(x-3)$

- Solve for "x".

By the Zero Product Property, you know that if $a* b = 0$, then $a=0$ or $b=0$.

Then you get:

$x=-1\ or\ x=3$

- Choose the positive value ($x=3$)

Then, Ana will hit the water after 3 seconds.