Final answer:
The average rate of change of a quadratic equation over an interval can be found by calculating the difference in the function values at the endpoints of the interval and dividing it by the difference in the x-values of the endpoints.
Step-by-step explanation:
The average rate of change of a quadratic equation over an interval can be found by calculating the difference in the function values at the endpoints of the interval and dividing it by the difference in the x-values of the endpoints. In this case, the interval is -1 ≤ x ≤ 5.
Let's consider the quadratic equation as an example: y = ax^2 + bx + c.
To find the average rate of change, we need to evaluate the equation at the endpoints of the interval. So, substitute -1 and 5 into the equation to find the corresponding y-values. Let's say the y-values at -1 and 5 are y1 and y2, respectively.
The average rate of change, denoted by ARC, is calculated using the formula: ARC = (y2 - y1) / (5 - (-1)).
For example, suppose the values of y at -1 and 5 are -2 and 10, respectively. Then, the average rate of change would be (10 - (-2)) / (5 - (-1)) = 12 / 6 = 2.