Question

The table shows values for a quadratic function.

Answer 1

The average rate of change for this function for the interval from x = 1

to x = 3 will be 8. Therefore option B is correct.

How to find the average rate of change of something?

Let the thing that is changing be y and the thing with which the rate is being compared is x, then we have the average rate of change of y as x changes as:

$\text{Average rate} = \dfrac{y_2 - y_1}{x_2 - x_1}$

where when

$x = x_1, y = y_1\\and \\x = x_2, y = y_2$

The average rate of change can be calculated as;

From x=1 to x=3,

y = 2 and y = 18

Therefore, based on the table, when:

$x_1 = 1 y_1 = 2 \\and \\x_2 = 3, y_2 = 18$

Then:

$\text{Average rate} = \dfrac{y_2 - y_1}{x_2 - x_1}$

$\text{Average rate} = \dfrac{18 - 2}{3-1}\\\\\text{Average rate} = \dfrac{16}{2}\\\\\text{Average rate} = 8$

Therefore option B is correct.

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