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;
[tex]y = a {x}^{2} + 3[/tex]
To find the value of 'a' we substitute any other point from the table say (1,2) to get:
[tex]2 = a( {1)}^{2} + 3[/tex]
[tex]a = 2 - 3 = - 1[/tex]
Hence the function is
[tex]y = - {x}^{2} + 3[/tex]
Now
[tex]f(10) = - 100 + 3 = - 97[/tex]
[tex]f(9) = - 81 + 3 = - 78[/tex]
The average rate of change from x=9 to x=10 is
[tex] \frac{f(10) - f(9)}{10 - 9} = \frac{ - 97 - - 78}{1} = - 19[/tex]
