Answer
$f(a)=3-5a+4a^{2}$
$f(a+h)=3-5a-5h+4a^{2}+8ah +4h^{2}$
$\frac{f(a+h)-f(a)}{h}=8a+4h-5$
Work Step by Step
We are given $f(x)=3-5x+4x^{2}$
We evaluate:
$f(a)=3-5a+4a^{2}$'
$f(a+h)=3-5(a+h)+4(a+h)^{2}=3-5a-5h+4a^{2}+8ah +4h^{2}$
$\frac{f(a+h)-f(a)}{h}=\frac{3-5a-5h+4a^{2}+8ah +4h^{2}-3+5a-4a^{2}}{h}=\frac{-5h+8ah+4h^{2}}{h}=8a+4h-5$
