Question

This table shows values that represent a quadratic function.

What is the average rate of change for this quadratic function for the interval from x=3 to x=5?

A. -16

B. 16

C. -8

D. 8

Answer 1

To find the average rate of change for a quadratic function over a given interval, we need to calculate the slope of the line connecting the two endpoints of the interval.

In this case, the interval is from x = 3 to x = 5. Let's denote the function as f(x).

The average rate of change is given by the formula: (f(5) - f(3))/(5 - 3).

To find f(5), substitute x = 5 into the quadratic function. To find f(3), substitute x = 3 into the quadratic function.

Once you have these values, calculate the difference between f(5) and f(3), and divide it by the difference between 5 and 3.

Finally, simplify the expression and determine the correct option from the given choices.