Question

An astronaut on the moon drops a tool from the door of the landing ship. The quadratic function f(x)=-2x^2+10 models the height of the tool, in meters, after x seconds. How long does it take the tool to hit the surface of the moon? Round your answer to the nearest tenth.

Answer 1

2.2 seconds.

Explanation:

We have been given that an astronaut on the moon drops a tool from the door of the landing ship. The quadratic function
`f(x)=-2x^2+10` models the height of the tool, in meters, after x seconds.

To find the time, it will take for the tool to hit the surface of moon, we will set
`f(x)=0` and solve for x as:

`-2x^2+10=0`

`-2x^2+10-10=0-10`

`-2x^2=-10`

Divide both sides by negative 2:

`(-2x^2)/(-2)=(-10)/(-2)`

`x^2=5`

Now, we will take square root of both sides:

`√(x^2)=\pm√(5)`

`x=\pm 2.236067`

`x\approx 2.2`

Since time cannot be negative therefore, it will take 2.2 seconds for the tool to hit the surface of the moon.