Question

Image of question provided

Answer 1

Answer:

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

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

$12=-3a\\a=\frac{12}{-3}\\ a=-4$

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.

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