The average rate of change of the given quadratic function on the interval
[tex]0\le x\le4[/tex]
is the slope of the secant line connecting the points
[tex](0,f(0))\text{ and (4,f(4)}[/tex]
In other words, the average rate of change is
[tex]m=\frac{f(4)-f(0)}{4-0}[/tex]
From the graph, we can see that f(0)=0 and f(4)=-4. By substituying these values into the last equation, we obtain
[tex]\begin{gathered} m=\frac{-4-0}{4-0} \\ m=-\frac{4}{4} \\ m=-1 \end{gathered}[/tex]
Hence the average rate of change for the given quadratic function whose graph is shown on 0≤x≤4 is -1
