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To find the average rate of change of the function \( h(x) \) from \( x = 4 \) to \( x = 8 \), we need to calculate the slope between the points on the graph corresponding to \( x = 4 \) and \( x = 8 \). This is the formula for average rate of change:

\[
\text{Average Rate of Change} = \frac{h(8) - h(4)}{8 - 4}
\]

### Step 1: Determine \( h(4) \) and \( h(8) \)
Looking at the graph, observe the function values at \( x = 4 \) and \( x = 8 \).

- \( h(4) = 4 \) (the function value when \( x = 4 \))
- \( h(8) = 0 \) (the function value when \( x = 8 \))

### Step 2: Apply the values to the formula
Now substitute the values into the formula:

\[
\text{Average Rate of Change} = \frac{0 - 4}{8 - 4} = \frac{-4}{4} = -1
\]

### Final Answer:
The average rate of change of \( h(x) \) from \( x = 4 \) to \( x = 8 \) is \( -1 \).

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Would you like further details on how average rate of change relates to slopes, or do you have any other questions?

Here are 5 related questions to consider:
1. What does the negative average rate of change indicate about the function’s behavior?
2. How does the rate of change differ between intervals on a graph of a quadratic function?
3. Could the average rate of change for any quadratic function be zero?
4. How does the average rate of change relate to the concept of the derivative in calculus?
5. What would happen if we calculated the average rate of change over a smaller interval?

**Tip:** The average rate of change over an interval of a quadratic function gives the slope of the secant line between two points on the curve.

Use the graph of the function to find its average rate of change from x = 4 to x = 8.

Learn how to find the average rate of change for a function using its graph from x = 4 to x = 8. This example involves calculating the slope between two points, providing insights into key algebraic concepts. Suitable for students in Grades 9-10.

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