Question

This table represents a quadratic function with a vertex at (1,1). What is the average rate of change for the interval from x=5 to x=6 ?

Answer 1

top answer is correct.

Explanation:

Answer 2

C. 9

Explanation:

The vertex form of the function is given by;

`f(x)=a(x-h)^2+k`

where
`(h,k)=(1,1)` is the vertex of the parabola.

`f(x)=a(x-1)^2+1`

We substitute a third point say, (3,5) to find the value of a;

`5=a(3-1)^2+1`

`5-1=a(2)^2`

`4=4a`

`1=a`

The function is

`f(x)=(x-1)^2+1`

`f(6)=(6-1)^2+1`

`f(6)=(5)^2+1`

`f(6)=26`

The average rate of change for the interval x=5 to x=6 is

`=(f(6)-f(5))/(6-5)`

`=(26-17)/(1)`

`=9`