Question

How do you find f(x+h) for the function `f(x)= x^2 - 2x + 5`?

Answer 1

see explanation.

Explanation:

To find f(x+h) substitute x = x + h into the function.

`f(color(red)(x+h))=(color(red)(x+h))^2-2(color(red)(x+h))+5`

now distribute the brackets

`f(x+h)=x^2+2hx+h^2-2x-2h+5`

which may be expressed as

`f(x+h)=x^2+2x(h-1)+h^2-2h+5`