Find and simplify the difference quotient

Question

find and simplify the different quotient F(x+h)-f(x)/h for the following function

f(x)=ax^2 + bx + c where a DOES NOT equal 0

Answer 1

[f(x+h) - f(x)] / h = [a(x+h)² + b(x+h) + c - (ax² + bx + c)] / h =

[ax² + 2axh + ah² + bx + bh + c - ax² - bx - c] / h = (2axh + ah² + bh) / h = h(2ax + ah + b) / h = 2ax + ah + b