Answer:
C. 9
Step-by-step explanation:
The vertex form of the function is given by;
[tex]f(x)=a(x-h)^2+k[/tex]
where [tex](h,k)=(1,1)[/tex] is the vertex of the parabola.
[tex]f(x)=a(x-1)^2+1[/tex]
We substitute a third point say, (3,5) to find the value of a;
[tex]5=a(3-1)^2+1[/tex]
[tex]5-1=a(2)^2[/tex]
[tex]4=4a[/tex]
[tex]1=a[/tex]
The function is
[tex]f(x)=(x-1)^2+1[/tex]
[tex]f(6)=(6-1)^2+1[/tex]
[tex]f(6)=(5)^2+1[/tex]
[tex]f(6)=26[/tex]
The average rate of change for the interval x=5 to x=6 is
[tex]=\frac{f(6)-f(5)}{6-5}[/tex]
[tex]=\frac{26-17}{1}[/tex]
[tex]=9[/tex]
