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) How many seconds after diving will Ana hit the water?

Answer 1

She will hit the water after 3 seconds.

We first set the function equal to 0:
0=-5(x+1)(x-3)

Using the zero product property, we know that either x+1=0 or x-3=0. Therefore our options are x=-1 or x=3. Since x represents time, -1 makes no sense; therefore the answer is x=3.

Answer 2

She will hit the water after 3 seconds.

Explanation:

Given,

Ana's height above water is modeled by,

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

Where, x is the number of seconds after diving.

When, she hit water, h(x) = 0

`\implies -5(x+1)(x-3) = 0`

`\implies (x+1)(x-3)=0` ( Dividing both sides by -5 )

By zero product property,

`(x+1)=0\text{ or } x-3=0`

⇒ x = - 1 or x = 3

Since, time can not be negative,

So, x = 3

Hence, she will hit the water after 3 seconds.