Question

The function f(x) = –2x2 + 32 represents the height of an object, f(x), after x seconds. How many seconds does it take for the object to hit the ground?

Answer 1

Given:

The height of an object, f(x), after x seconds is

$f(x)=-2x^2+32$

To find:

The time taken be object to hit the ground.

Solution:

We have,

$f(x)=-2x^2+32$

The object will hit the ground if the height is 0, i.e., f(x)=0.

$0=-2x^2+32$

$2x^2=32$

Divide both sides by 2.

$x^2=\dfrac{32}{2}$

$x^2=16$

Taking square root on both sides.

$x=\pm 4$

Time cannot be negative. So, x=4.

Therefore, the object will hit the ground after 4 seconds.