The graph shows the quadratic function f(x) . What is the average rate of change for the quadratic function from x = 10 to x = 12? Enter your answer in the box.
Accepted Solution
A:
Since you have not shown the quadratic function, I will explain you the procedure to calculate the average rate of change with any quadratic function and you will be able to apply the system to you own quadratic function.
Explanation:
1) The average rate of change is the total (net) change of the function divided by the time elapsed (or the distance between the two input data).
2) For example, given:
Initial value of the function, for t = a: f(a) Final value of the function, for t = b: f(b)
Then, the average rate of change = change on the function / change on hte input variable = [ f(b) - f(a) ] / [ b - a]
3) This is an example with a quadratic function:
f(x) = 3x^2 - 2x + 20
for x = 10, f(10) = 3 (10)^2 - 2(10) + 20 =3(100) - 20 + 20 = 300
for x = 12, f(12) = 3 (12)^2 - 2(12) + 20 = 3(144) -24 + 20 = 428
This very same procedure you can use whenever you know the function.
If what you have is the graph of the function, just take f(12) and f(10) from the graph, and calculate [f(12) - f(10) ] / (12 - 10) = [ f(12) - f(10) ] / 2.