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O GRAPHS AND FUNCTIONSFinding a difference quotient for a linear or quadratic fun

O GRAPHS AND FUNCTIONSFinding a difference quotient for a linear or quadratic fun-example-1
User Brad Dwyer
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1 Answer

13 votes
13 votes

Step-by-step explanation:

We know that f(x) = - x² + x - 6

Then, we can find f(x + h) as follows:

f(x + h) = -(x + h)² + (x + h) - 6

f(x + h) = -(x² + 2xh + h²) + x + h - 6

f(x + h) = -x² - 2xh - h² + x + h - 6

Then, we can find the difference quotient as


(f(x+h)-f(x))/(h)=\frac{(-x^2-2xh-h^2+x+h-6)-(-x^2+x-6)_{}}{h}

Simplifying, we get:


\begin{gathered} =(-x^2-2xh-h^2+x+h-6+x^2-x+6)/(h) \\ =(-2xh-h^2+h)/(h) \\ =-2x-h+1 \end{gathered}

Therefore, the answer is


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User Smallpepperz
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