Question

These tables represent a quadratic function with a vertex at (0,3). What is the average rate of change for the interval from X =9 to x= 10?

Answer 1

-19

Explanation:

Answer 2

-19

Explanation:

The missing table is shown in the attachment.

Since the quadratic function has vertex at (0,3), its equation is of the form;

`y = a {x}^(2) + 3`

To find the value of 'a' we substitute any other point from the table say (1,2) to get:

`2 = a( {1)}^(2) + 3`

`a = 2 - 3 = - 1`

Hence the function is

`y = - {x}^(2) + 3`

Now

`f(10) = - 100 + 3 = - 97`

`f(9) = - 81 + 3 = - 78`

The average rate of change from x=9 to x=10 is

`(f(10) - f(9))/(10 - 9) = ( - 97 - - 78)/(1) = - 19`