Question

The vertical height in feet of a projectile on a planet in our solar system at a given time t in seconds is represented by the function h(t)=−6t2+24t . Re-write h(t) in the form h(t)=a(t-h)^2+k and determine the maximum height of the projectile. Show all work.

Answer 1

We are given the following function:

`h(t)=-6t^2+24t`

We will take "-6" as a common factor:

`h(t)=-6(t^2-4t)`

Now, we will complete the square in the expression inside the parenthesis by adding and subtracting the following term: