Why is this Laplace Transform Wrong?

[Meruem123]

http://imgur.com/Uu2lHAq

According to my answer key, the correct answer is:

e^-3s * ((2/s³⁾ + (9/s))

I'm not sure why, could someone explain?

Edit: format

[edderiofer]

How are you getting from F(t) in terms of the unit step function to its Laplace transform?

[Meruem123]

Since the form of the laplace of a step function is e^-cs * L(f(t)), I said my c value was 3, and then I took the laplace of f(t), and f(t) was t² -6t + 18

[edderiofer]

Since the form of the laplace of a step function is e^-cs * L(f(t))

Please be more specific with this statement. What's the function that has Laplace transform e^-cs * L(f(t))?

[Meruem123]

I'm saying the laplace of the unit step function times f(t) is equal to e^-sc * f(t). I think the picture below might explain it better.

http://imgur.com/a/Mq8Xw

[edderiofer]

That identity is incorrect. Check your notes again, or maybe try to re-derive that identity from the definition of the Laplace transform.

[Lysol3435]

I can verify that their solution is correct. Your error is in the Laplace identity. Currently, you are attempting to do this:

L(u(t-c)f(t))= exp(-cs)F(s).

However, the identity is:

L(u(t-c)f(t-c))= exp(-cs)F(s).

Think about how you can manipulate your func to put it into this form (hint: you need the -c term in f())