For the function $f(x)=2 x^{2}-2 x-4$, evaluate and fully simplify each of the following.
\[
f(x+h)=
\]
\[
\frac{f(x+h)-f(x)}{h}=
\]
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Final Answer: The difference quotient of the function \(f(x)=2 x^{2}-2 x-4\) is \(\boxed{4x + 2h - 2}\)
Step 1 ：Given the function \(f(x)=2 x^{2}-2 x-4\)
Step 2 ：Substitute \(x+h\) into the function to get \(f(x+h)=2(x+h)^{2}-2(x+h)-4\)
Step 3 ：Simplify to get \(f(x+h)=2x^{2}+4hx+2h^{2}-2x-2h-4\)
Step 4 ：Subtract the function at \(x\) from \(f(x+h)\) to get \(f(x+h)-f(x)=(2x^{2}+4hx+2h^{2}-2x-2h-4)-(2x^{2}-2x-4)\)
Step 5 ：Simplify to get \(f(x+h)-f(x)=4hx+2h^{2}-2h\)
Step 6 ：Divide by \(h\) to get the difference quotient \(\frac{f(x+h)-f(x)}{h}=4x+2h-2\)
Step 7 ：Final Answer: The difference quotient of the function \(f(x)=2 x^{2}-2 x-4\) is \(\boxed{4x + 2h - 2}\)
