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

Answer:

-19

Step-by-step 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

$\frac{f(10) - f(9)}{10 - 9} = \frac{ - 97 - - 78}{1} = - 19$