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 = 9 to x = 10?

Answer 1

A. -19

Explanation:

Answer 2

A. -19

Explanation:

There are lots of ways to get there. One of them is to realize that the average rate of change between two adjacent numbers is the negative of their sum. -(9+10) = -19.

__

Another is to extend the table:

6 to 7 : -13

7 to 8 : -15

8 10 9 : -17

9 to 10 : -19

__

Yet another is to write an equation for the function, and compute the average rate of change:

f(x) = -x^2 -1

average rate of change from 9 to 10 = (f(10) -f(9))/(10 -9) = (-101 -(-82))/(10 -9) = -19