Whats the average rate of change between x=6 and x=-6 for
f(x)=8x^2+1x+10
Hello, sadieann!
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Find the average rate of change between $\displaystyle x=\text{-}6$ and $\displaystyle x=6$ for $\displaystyle f(x)\:=\:8x^2+1x+10$
$\displaystyle \begin{array}{cccccc}\text{When }x=\text{-}6\!: &f(\text{-}6) &=& 8(\text{-}6)^2 + (\text{-}6) + 10 &=& 292 \\
\text{When }x = 6\!: & f(6) &=& 8(6^2) + 6 + 10 &=& 304\end{array}$
The function changed by: $\displaystyle f(6) - f(\text{-}6) \:=\:304 - 292 \:=\:+12$ units
. . over a distance of: $\displaystyle 6 - (\text{-}6) \:=\:12$ units.
Therefore, the average rate of change is: .$\displaystyle \frac{12}{12} \:=\:1$