Difference Quotient of x^2-2x

(x+h)^2-2(x+h)-(x^2-2x) / h
x^2+2xh+h^2-2x-2h-x^2+2x / h

x^2 cancel out
2x cancel out
h and -2h cancel and leave -2

result: h^2+2xh-2

I believe you forgot to divide the h^2 by h.

result:
(h^2+2xh-2h)/h
= h+2x-2

ok that makes sense. Thanks for the help

To find the difference quotient of the function f(x) = x^2 - 2x, we can use the formula:

[f(x+h) - f(x)] / h

Let's break down the steps to find the difference quotient for this function:

Step 1: Substitute f(x+h) and f(x) into the formula.
[f(x+h) - f(x)] / h = [(x+h)^2 - 2(x+h) - (x^2 - 2x)] / h

Step 2: Expand and simplify the numerator.
[(x^2 + 2xh + h^2) - 2x - 2h - x^2 + 2x] / h

Step 3: Simplify the numerator further by combining like terms.
(x^2 - x^2) + (2x - 2x) + (h^2 - 2h) / h

Step 4: Cancel out the like terms in the numerator.
0h + 0 + h^2 - 2h / h

Step 5: Simplify the expression in the numerator.
h^2 - 2h / h

So the difference quotient of f(x) = x^2 - 2x is h^2 - 2h / h.