Find the average rate of change of the quadratic function f(x) over the interval -2 less than or equal to x less than or equal to 3. Use the following table, which shows the values of the function for various values of x.
-3, 60
-2, 25
3, 0
4, 25
To find the average rate of change of the quadratic function f(x) over the interval -2 ≤ x ≤ 3, we use the formula:
Average Rate of Change = (f(3) - f(-2)) / (3 - (-2))
From the table:
f(3) = 0
f(-2) = 25
Substitute these values into the formula:
Average Rate of Change = (0 - 25) / (3 - (-2))
Average Rate of Change = (-25) / 5
Average Rate of Change = -5
Therefore, the average rate of change of the quadratic function f(x) over the interval -2 ≤ x ≤ 3 is -5.