Given:
The height of an object, f(x), after x seconds is
[tex]f(x)=-2x^2+32[/tex]
To find:
The time taken be object to hit the ground.
Solution:
We have,
[tex]f(x)=-2x^2+32[/tex]
The object will hit the ground if the height is 0, i.e., f(x)=0.
[tex]0=-2x^2+32[/tex]
[tex]2x^2=32[/tex]
Divide both sides by 2.
[tex]x^2=\dfrac{32}{2}[/tex]
[tex]x^2=16[/tex]
Taking square root on both sides.
[tex]x=\pm 4[/tex]
Time cannot be negative. So, x=4.
Therefore, the object will hit the ground after 4 seconds.
