Your answer is incorrect. Find the difference quotient $\frac{f(x+h)-f(x)}{h}$, where $h \neq 0$, for the function below. \[ f(x)=-4 x^{2}-2 x+1 \] Simplify your answer as much as possible. \[ \frac{f(x+h)-f(x)}{h}= \] Check

Step 1 ：The difference quotient is a measure of the average rate of change of the function over the interval h. To find the difference quotient for the function \(f(x) = -4x^2 - 2x + 1\), we need to substitute \(x+h\) into the function for \(x\), subtract the original function, and then divide by \(h\).

Step 2 ：Substitute \(x+h\) into the function for \(x\): \(f(x+h) = -4(x+h)^2 - 2(x+h) + 1\).

Step 3 ：Subtract the original function: \(f(x+h) - f(x) = -4(x+h)^2 - 2(x+h) + 1 - (-4x^2 - 2x + 1)\).

Step 4 ：Divide by \(h\) to get the difference quotient: \(\frac{f(x+h)-f(x)}{h} = \frac{-4(x+h)^2 - 2(x+h) + 1 - (-4x^2 - 2x + 1)}{h}\).

Step 5 ：Simplify the difference quotient to get the final answer: \(\frac{f(x+h)-f(x)}{h} = -4h - 8x - 2\).

Step 6 ：Final Answer: The simplified difference quotient for the function \(f(x) = -4x^2 - 2x + 1\) is \(\boxed{-4h - 8x - 2}\).