Answer
$8a+4h-5$
Work Step by Step
$f(x)=3-5x+4x^{2}$
Find $f(a)$ by substituting $x$ with $a$:
$f(a)=3-5a+4a^{2}$
Find $f(a+h)$ by substituting $x$ with $a+h$:
$f(a+h)=3-5(a+h)+4(a+h)^{2}=...$
$...=3-5a-5h+4(a^{2}+2ah+h^{2})=...$
$...=3-5a-5h+4a^{2}+8ah+4h^{2}$
We have $f(a)$ and $f(a+h)$, we can now substitute them in the expression $\dfrac{f(a+h)-f(a)}{h}$.
$\dfrac{3-5a-5h+4a^{2}+8ah+4h^{2}-3+5a-4a^{2}}{h}=...$
Combine like terms in the numerator:
$...=\dfrac{-5h+8ah+4h^{2}}{h}=...$
Take out common factor $h$ from the numerator and simplify:
$...=\dfrac{h(-5+8a+4h)}{h}=8a+4h-5$
