To find the average rate of change of the function over the interval $-1 \leq x \leq 2$, we need to evaluate the change in $y$-values over this interval and divide it by the change in $x$-values.

1. Identify Points on the Graph: From the graph:

   • At $x = -1$, the corresponding $y$-value appears to be around $3$.
   • At $x = 2$, the corresponding $y$-value appears to be $0$.

2. Calculate the Average Rate of Change: The average rate of change formula is: $\frac{f(x_2) - f(x_1)}{x_2 - x_1}$ where $x_1 = -1$ and $x_2 = 2$.

   Substituting the values we found: $\frac{f(2) - f(-1)}{2 - (-1)} = \frac{0 - 3}{2 + 1} = \frac{-3}{3} = -1$

So, the average rate of change of the function over the interval $-1 \leq x \leq 2$ is -1.

Would you like a detailed explanation or further assistance with this concept?

Here are five questions to expand on this concept:

1. What is the significance of a negative average rate of change?
2. How can you interpret the slope of a line segment between two points on a curve?
3. How does the average rate of change differ from the instantaneous rate of change?
4. What does it mean if the average rate of change over an interval is zero?
5. Can the average rate of change be used to estimate the behavior of a nonlinear function?

Tip: For parabolic graphs, the average rate of change between two points can give insight into the general direction of the curve over that interval.