Help!!
f(x+8) = (x + 8)2-5x(x+8)+1

Question

Help!! 
f(x+8) = (x + 8)2-5x(x+8)+1

myininaya · Answer

I'm having trouble figuring out what you need here.

myininaya · Answer

What are the instructions or directions?

anonymous · Answer

to solve it

anonymous · Answer

it ended up being x2 + 11x +25  but i dont know how

myininaya · Answer

?
What are we solving for?

myininaya · Answer

Do you mean you want to simplify f(x+8)?

anonymous · Answer

yes thank you that helps

myininaya · Answer

$$(x+8)^2-5x(x+8)+1=(x^2+16x+64)-5x(x+8)+1$$
$$=(x^2+16x+64)-5x^2-40x+1=x^2-5x^2+16x-40x+64+1$$
$$-4x^2-24x+65$$

myininaya · Answer

without that extra x in there you would get what you got above

anonymous · Answer

what you want to find?

anonymous · Answer

I guess, people mostly ask us to find critical points for this type of questions.

So, by solving RHS, you get $$−4x2−24x+65$$

1. Let us differentiate LHS and RHS.

$$d/dx (f(x+8) ) = d/dx ( −4x2−24x+65) $$
at max and min points, LHS = 0. so, equate RHS to 0 to find the points at which LHS=0; so the critical points.

Note: I think, there must be some range given, so take only the critical points which are in that range. If range isn't given.. take them all.

2. Other critical points are where f(x+8) is undefined.

as its a polynomial.. it is defined for all R. 

So, you should be getting 2 critical points.

anonymous · Answer

Well, if you want to find $$f(x) $$ from it.. its very simple.. 
substitute  

so, the above equation $$f(x+8) = (x + 8)^2-5x(x+8)+1$$ becomes 

$$f(x-8+8) = (x-8 + 8)^2-5(x-8)(x-8+8)+1$$

$$=> f(x) = x^2 -5(x-8)(x)+1$$
$$=> f(x) = x^2 -5x^2 +40x+1$$
$$=> f(x) =-4x^2 +40(x)+1$$

* please do check if there are any arithmetic errors (minor +/-)..
However, the basic structure and method is right

anonymous · Answer

thank you very much

anonymous · Answer

I forgot to mention a word in my above answer [in 5th lin3] .
"substitute x = x-8