Question

Find and simplify the expression if f(x)=x^2-10.

f(4+h)-f(4)=

Answer 1

`f(4+h)-f(4)=(4+h)^2-10-(4^2-10)\\f(4+h)-f(4)=16+8h+h^2-10-16+10\\f(4+h)-f(4)=h^2+8h`

Answer 2

`f (4 + h) -f (4) = h ^ 2 + 8h`

Explanation:

We have the following quadratic function.

`f (x) = x ^ 2-10`

We must find the following expression

`f (4 + h) -f (4) =`

First we must find
`f (4 + h)`

Then substitute
`x = (4 + h)` in the quadratic equation:

`f (4 + h) = (4 + h) ^ 2 -10\\\\f (4 + h) = 16 + 8h + h ^ 2 -10\\\\f (4 + h) = h ^ 2 + 8h +6`

Now we find
`f(4)`. Replace
`x = 4` in the function
`f (x)`

`f (4) = (4) ^ 2-10\\\\f (4) = 16-10\\\\f (4) = 6`

Finally we have to:

`f (4 + h) -f (4) = h ^ 2 + 8h +6 - 6`

`f (4 + h) -f (4) = h ^ 2 + 8h`