Question

Image of question provided

Answer 1

To solve this problem, we can use a system of equations.

We know the quadratic expression has the form

`f(t)=at^(2)+bt`

Using points (1,12) and (4,0), we can form the following system to find a and b.

`12=a+b`

`0=16a+4b`

We need to divide the second equation by -4 and sum both equations

`12=a+b\\0=-4a-b`

`12=-3a\\a=(12)/(-3)\\ a=-4`

Then, we use this value to find the other variable

`12=a+b\\12=-4+b\\b=12+4\\b=16`

Therefore, the quadratic function that models the situation is

`f(t)=-4t^(2) +16t` or
`f(t)=-4t(t-4)`

According to this expression, after 2 seconds, the height is 16 feet.

`f(2)=-4(2)(2-4)=-8(-2)=16`