Question

Use the graph below to answer the following question: graph of parabola going through 0, 4, 2, negative 4, and 4, 4 What is the average rate of change from x = 0 to x = 4?

Answer 1

Answer:

The average rate of change from x = 0 to x = 4 is 0.

Step-by-step explanation:

Given information: The graph of parabola passes through the points (0,4), (2,-4) and (4,4).

The average rate of change of a function between x₁ and x₂ is

$m=\frac{f(x_2)-f(x_1)}{x_2-x_1}$

We need to find the average rate of change from x = 0 to x = 4.

$m=\frac{f(4)-f(0)}{4-0}$

The value of function is 4 at x=4 and x=0.

$m=\frac{4-4}{4}$

$m=\frac{0}{4}$

$m=0$

Therefore the average rate of change from x = 0 to x = 4 is 0.

Answer 2

The average rate of change is equivalent to the slope of the graph between the two points.slope = change in y / change in xdy/dx = (-5 - 3) / (2 - 0)dy/dx = -4
The average rate of change from x = 0 to x = 2 is -4.
hope this helps