Question

what is the average rate of change for this quadratic function for the interval from x = 0 to x = 2? a. 6 b. 2 c. 4 d. 3

Explanation:

Step1: Find the values of the function at \(x = 0\) and \(x = 2\)

From the graph, when \(x = 0\), \(y_1=2\); when \(x = 2\), \(y_2 = 6\).

Step2: Use the average - rate - of - change formula

The formula for the average rate of change of a function \(y = f(x)\) over the interval \([a,b]\) is \(\frac{f(b)-f(a)}{b - a}\). Here, \(a = 0\), \(b = 2\), \(f(0)=2\), \(f(2)=6\). Then the average rate of change is \(\frac{6 - 2}{2-0}=\frac{4}{2}=2\).

Answer:

B. 2