Question

The path of a breaching ocra whale can be modeled by the function k(x) = x^2 - 2x - 8, where x is the time elapsed in seconds under water, and k(x) is the height in ft below the water.

Determine HOW LONG is the ocra (killer) whale underwater to the nearest second. MUST BE SOLVED ALGEBRAICALLY!

Answer 1

The time duration of the ocra whale spends under water is 4 seconds

Explanation:

The equation that model the path of the ocra whale is presented as follows;

k(x) = x² - 2·x - 8

Where;

x = The time elapsed in seconds under water

k(x) = The height in feet below water

Therefore, the point where the ocra whale enters the water, k(x) = 0

At the point of submerging below the water surface, we have;

k(x) = 0 = x² - 2·x - 8

Factorizing the quadratic equation gives;

0 = x² - 2·x - 8 = (x - 4)·(x + 2)

Therefore, when k(x) = 0, either;

(x - 4) = 0, which gives, x = 4

(x + 2) = 0, which gives, x = -2

Given that 'x' represent the time, the time elapsed while the whale is under water, x = 4 seconds