Find f(a + h) - f(a) for the function. Simplify your answer.
f(x)=x^2-9x+3.
I'm not exactly sure how to go about this...

Question

anonymous · Answer

first understand what 
$$f(a+h)$$ means. it means replace x everywhere you see it by 
$$a+h$$ so you get 
$$f(a+h)=(a+h)^2-9(a+h)+3$$

anonymous · Answer

and of course 
$$f(a)=a^2-9a+3$$

anonymous · Answer

so 
$$f(a+h)-f(a)=(a+h)^2-9(a+h)+3-(a^2-9a+3)$$ and it is algebra from here on in

anonymous · Answer

a bunch of algebra in fact 
$$a^2+2ah+h^2-9a-9h+3-a^2+9a-3$$
now the usual miracle occurs, everything without an h in it goes away and you get 
$$2ah-9h+h^2$$

anonymous · Answer

I see now.  I was forgetting how to start this type of problem, but right after your first post I realized what I had to do.  Thanks a ton!