Question

these tables represent a quadratic function with a vertex at (0, -1). what is the average rate of change for the interval from x = 7 to x = 8?

a. -50
b. -15
c. -65
d. -2

Explanation:

Step1: Find the pattern of the average rate of change

From the table of average rate of change, we can see that the average rate of change for each interval increases by \(- 2\) compared to the previous interval.

Step2: Calculate the average rate of change for \(x = 6\) to \(x=7\)

Since the average rate of change for \(x = 5\) to \(x = 6\) is \(-11\), then for \(x = 6\) to \(x=7\) it is \(-11-2=-13\)

Step3: Calculate the average rate of change for \(x = 7\) to \(x = 8\)

Since the average rate of change for \(x = 6\) to \(x = 7\) is \(-13\), then for \(x = 7\) to \(x = 8\) it is \(-13 - 2=-15\)

Answer:

B. \(-15\)