Question

This table represents a quadratic function with a vertex at (1, 0). What is the

average rate of change for the interval from x = 5 to x = 6?
a) 9
b) 7
c) 5
d) 25

Answer 1

The average rate of change for the interval from x = 5 to x = 6 can be calculated by taking the derivative of the quadratic function and evaluating it at the midpoint of the interval (x = 5.5).

Given that the vertex of the function is at (1, 0), the equation of the quadratic function is in the form of:

f(x) = a(x-1)^2 +0

The derivative of the function is:

f'(x) = 2ax - 2a

We know that the vertex of the function is at (1,0), which means that the value of a is 0.

So the derivative of the function is 0.

Therefore the average rate of change for the interval from x = 5 to x = 6 is 0.