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

Answer 1

To find the average rate of change for the interval from x = 7 to x = 8, we need to calculate the change in y divided by the change in x for that interval.

Let's first determine the values of y for x = 7 and x = 8 using the information given in the tables:

Table 1:
For x = 7, y = -2
For x = 8, y = -4

Table 2:
For x = 7, y = 4
For x = 8, y = 6

Now, calculate the change in y and change in x:
For Table 1:
Change in y = -4 - (-2) = -2
Change in x = 8 - 7 = 1

Average rate of change = Change in y / Change in x = -2 / 1 = -2

For Table 2:
Change in y = 6 - 4 = 2
Change in x = 8 - 7 = 1

Average rate of change = Change in y / Change in x = 2 / 1 = 2

Therefore, the average rate of change for the interval from x = 7 to x = 8 is -2 for Table 1 and 2 for Table 2.