Difference Quotient

Question

Find and simplify the difference quotient of f(x)= -2x^2 +3x +1

Answer 1

f(x) = -2x² + 3x + 1

[f(x+h) - f(x)] / h = [-2(x+h)² + 3(x+h) + 1 - (-2x² + 3x + 1)] / h

= [-2x² - 4xh - 2h² + 3x + 3h + 1 + 2x² - 3x - 1] / h

= [-4xh - 2h² + 3h] / h = h(-4x - 2h + 3) / h = -4x - 2h + 3