Question

A penguin leaps out of the water while swimming. This action is called porpoising. The height y (in feet) of a porpoising penguin can be modeled by y = −16x2 + 4.8x, where x is the time (in seconds) since the penguin leaped out of the water. Find the roots of the equation when y = 0. Explain what the roots mean in this situation.

Answer 1

Answer: The roots of the equation when y = 0 are 0 and 0.3

In this situation the root means the time (in seconds) since the penguin is inside the water.

Explanation:

Given: The height y (in feet) of a porpoising penguin can be modeled by

`y=-16x^2+4.8x`, where x is the time (in seconds) since the penguin leaped out of the water.

When y=0, then

`-16x^2+4.8x=0`

Taking 16x as common from both terms as gcf, we get

`16x(-x+0.3)=0\\\Rightarrow\ 16x=0\ or\ -x+0.3=0\\\Rightarrow\ x=0\ or\ x=0.3`

The roots of the equation when y = 0 are 0 and 0.3

In this situation the root means the time (in seconds) since the penguin is inside the water.