Answer:
[tex]f (4 + h) -f (4) = h ^ 2 + 8h[/tex]
Step-by-step explanation:
We have the following quadratic function.
[tex]f (x) = x ^ 2-10[/tex]
We must find the following expression
[tex]f (4 + h) -f (4) =[/tex]
First we must find [tex]f (4 + h)[/tex]
Then substitute [tex]x = (4 + h)[/tex] in the quadratic equation:
[tex]f (4 + h) = (4 + h) ^ 2 -10\\\\f (4 + h) = 16 + 8h + h ^ 2 -10\\\\f (4 + h) = h ^ 2 + 8h +6[/tex]
Now we find [tex]f(4)[/tex]. Replace [tex]x = 4[/tex] in the function [tex]f (x)[/tex]
[tex]f (4) = (4) ^ 2-10\\\\f (4) = 16-10\\\\f (4) = 6[/tex]
Finally we have to:
[tex]f (4 + h) -f (4) = h ^ 2 + 8h +6 - 6[/tex]
[tex]f (4 + h) -f (4) = h ^ 2 + 8h[/tex]
