not sure how to figure this one out

Question

Find f(a + h) - f(a) for the function. Simplify your answer.
f(x) = x^2 - 11 x + 9

Answer 1

f(x) = x² - 11 x + 9

 

f(a + h) - f(a)

 

f(a) =a²-11a+9

 

f(a+h) =(a+h)²-11(a+h) +9 = a²+2ah+h² -11a-11h+9

 

f(a + h) - f(a) = a²+2ah+h² -11a-11h+9 -(a²-11a+9)

 

                     = a²+2ah+h²-11a-11h+9 -a²+11a -9

                 

                     =2ah+h²-11h

                    

                     =h²+2ah-11h

 

Answer 2

I will give you the set up.  Then you can complete the rest.

 

f(x + h) - f(x) =

 

[(x + h)² - 11(x + h) + 9] - (x² - 11x + 9) =

 

[x² + 2xh + h² - 11x - 11h + 9] - x² + 11x - 9

 

 

Finish from here.