63.3k views
5 votes
What is the average rate of change of the quadratic equation over the interval - 1 ≤ x ≤ 5?

User Hugolpz
by
7.1k points

1 Answer

3 votes

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.

User Boris Prohaska
by
8.1k points