Question 994056
h, some small quantity which can be made as small as you wish be never being 0.


{{{f(x+h)=-10(x+h)^2+10(x+h)+8}}}
{{{-10(x^2+2hx+h^2)+10x+10h+8}}}
{{{-10x^2-20hx-10h^2+10x+10h+8}}}




Difference Quotient is
{{{(f(x+h)-f(x))/h}}}


{{{((-10x^2-20hx-10h^2+10x+10h+8)-(-10x^2 + 10x +8))/h}}}

{{{(-10x^2-20hx-10h^2+10x+10h+8+10x^2-10x-8)/h}}},  look at the terms in the numerator carefully....

{{{(-20hx-10h^2+10h)/h}}}

{{{highlight(-20x-10h+10)}}}
You might then ask, "what happens as h approaches 0?"