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

Answer:

C. 9

Step-by-step 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

$=\frac{f(6)-f(5)}{6-5}$

$=\frac{26-17}{1}$

$=9$