SOLUTION: The difference quotient, D, is defined by the equation D=f(x+h)-f(x)/h find D if f(x)=2x^2+7x+9

Algebra ->  Linear-equations -> SOLUTION: The difference quotient, D, is defined by the equation D=f(x+h)-f(x)/h find D if f(x)=2x^2+7x+9      Log On


   

Question 988892: The difference quotient, D, is defined by the equation D=f(x+h)-f(x)/h
find D if f(x)=2x^2+7x+9
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
f%28x%29=2x%5E2%2B7x%2B9


f%28x%2Bh%29=2%28x%2Bh%29%5E2%2B7%28x%2Bh%29%2B9


f%28x%2Bh%29=2%28x%5E2%2B2xh%2Bh%5E2%29%2B7%28x%2Bh%29%2B9


f%28x%2Bh%29=2x%5E2%2B4xh%2B2h%5E2%2B7x%2B7h%2B9


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D+=+%28f%28x%2Bh%29-f%28x%29%29%2Fh


D+=+%282x%5E2%2B4xh%2B2h%5E2%2B7x%2B7h%2B9-%282x%5E2%2B7x%2B9%29%29%2Fh


D+=+%282x%5E2%2B4xh%2B2h%5E2%2B7x%2B7h%2B9-2x%5E2-7x-9%29%2Fh


D+=+%284xh%2B2h%5E2%2B7h%29%2Fh


D+=+%28h%2A%284x%2B2h%2B7%29%29%2Fh


D+=+%28highlight%28h%29%2A%284x%2B2h%2B7%29%29%2F%28highlight%28h%29%29


D+=+%28cross%28h%29%2A%284x%2B2h%2B7%29%29%2F%28cross%28h%29%29


D+=+4x%2B2h%2B7


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The final simplified answer is D+=+4x%2B2h%2B7