Question

which is the best estimate for the average rate of change for the quadratic function graph on the interval
`0 \leqslant x \leqslant 4`

Answer 1

The average rate of change of the given quadratic function on the interval

`0\le x\le4`

is the slope of the secant line connecting the points

`(0,f(0))\text{ and (4,f(4)}`

In other words, the average rate of change is

`m=(f(4)-f(0))/(4-0)`

From the graph, we can see that f(0)=0 and f(4)=-4. By substituying these values into the last equation, we obtain

`\begin{gathered} m=(-4-0)/(4-0) \\ m=-(4)/(4) \\ m=-1 \end{gathered}`

Hence the average rate of change for the given quadratic function whose graph is shown on 0≤x≤4 is -1