Question

The function h(x) = -6x^3 + 12x^2 represents the approximate height of a kangaroo (x seconds) after it jumps. How many seconds is the kangaroo airborne?

Answer 1

Since h(x) represents the height of a kangaroo x seconds after it jumps, then the kangaroo is on the ground when h(x)=0.

Now, notice that:

`-6x^3+12x^2=-6x^2(x-2).`

Then:

`h(x)=0\text{ if and only if }-6x^2=0\text{ or }x-2=0.`

Therefore:

`h(x)=0\text{ if and only if }x=0\text{ or }x=2.`

Then the kangaroo is in air for 2 seconds.

Answer: 2 seconds.