Question:
Solution:
Consider the following function:
[tex]h(x)=-3(x-3)^2+108[/tex]
where x is measure in seconds and h(x) represents the height of the object. Now, if the hovercraft land on the ground then h(x) = 0. Thus, we get:
[tex]0=-3(x-3)^2+108[/tex]
Our goal is to solve this for x. Expanding the square we have that the above equation is equivalent to:
[tex]0=-3(x^2-6x+9)^{}+108[/tex]
applying the distributive property we obtain:
[tex]0=-3x^2+18x-27^{}+108[/tex]
this is equivalent to:
[tex]0=-3x^2+18x+81[/tex]
or
[tex]-3x^2+18x+81\text{ = 0}[/tex]
Using the quadratic formula we obtain that the solutions of this equation are:
[tex]x\text{ = -3 and }x=\text{ 9}[/tex]
Note that by convention time is positive, therefore the correct answer is
[tex]x\text{ = 9 }[/tex]
