Question

The table of values represents a quadratic function.

What is the average rate of change for f(x) from x=−10 to x = 0?



Enter your answer in the box.

x ​f(x)
​
​−10
​ 184
​−5
​ 39
0 ​−6
​
5 49
10 204

Answer 1

To find the average rate of change of the function \(f(x)\) from \(x = -10\) to \(x = 0\), we can use the formula:

\[
\text{Average Rate of Change} = \frac{f(b) - f(a)}{b - a}
\]

where \(a = -10\) and \(b = 0\).

From the table, we have the following values:

- \(f(-10) = 184\)
- \(f(0) = -6\)

Now substituting these values into the formula:

\[
\text{Average Rate of Change} = \frac{f(0) - f(-10)}{0 - (-10)} = \frac{-6 - 184}{0 + 10} = \frac{-190}{10} = -19
\]

Thus, the average rate of change for \(f(x)\) from \(x = -10\) to \(x = 0\) is \(\boxed{-19}\).