Question

The table shows values for a quadratic function. What is the average rate of change for this function for the interval from x=2 to x=4

Answer 1

Answer: OPTION C.

Step-by-step explanation:

In order to find the  average rate of change for this function for the given quadratic function, for the interval from $x=2$ to $x=4$, you can use this formula:

$average\ rate\ of\ change$$=\frac{f(b)-f(a)}{b-a}$

In this case, you can identify that:

$f(b)=8\\f(a)=32\\\\b=2\\\\a=4$

Then, substituting values into the formula, you get this result:

 $average\ rate\ of\ change=\frac{8-32}{2-4}=12$

This matches with the option C.

Answer 2

ANSWER

C. 12

EXPLANATION

The average rate of change of a function ,f(x) from x=a to x=b is given by:

$\frac{f(b) - f(a)}{b - a}$

We want to find the average rate of change of the quadratic function represented by the table for the interval from x=2 to x=4.

From the table, we have

$f(4) = 32$

and

$f(2) = 8$

The average rate of is

$\frac{f(4) - f(2)}{4 - 2} = \frac{32 - 8}{2} = \frac{24}{2} = 12$

Geometrically, the average rate of change represents the slope of the secant line joining the points (4,32) and (2,8) on the given quadratic function.

The correct choice is C.