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

Answer:

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

Step-by-step 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:

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

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