Question

Hi! Hope you're having a good day. So, there's a problem I had gotten wrong while I was preparing for the ACT, however, I didn't know how to answer the question to begin with. Can someone give me a step-by-step explanation on how this problem is solved correctly? (Picture included). Inside of the picture I included the answer I chose and the correct answer, could you also explain what I had done wrong? I used the FOIL method, but now I think that was incorrect to begin with. I also reattempted to do what I had done before, but each time I get a different answer, if you can help that'd be fantastic! :)

Answer 1

Answer:

$3a^2+12a+12$

Step-by-step explanation:

first, you have to plug in x = a+2 into the function, which would look like:

$f(a+2) =3(a+2)^2$

then, you can first simplify $(a+2)^2$. to do this, use the rule $(a+b)^2 = a^2 +2ab + b^2$, so it would be $a^2+(2*a*2)+2^2 = a^2 + 4a + 4$

this means your new equation is:

$3(a^2+4a+4)$

you can then distribute the 3:

$3*a^2+3*4a + 3*4 = 3a^2+12a+12$

let me know if there's anything you want me to clarify!