calculating a rate of change of a quadratic function over an interval\nwhat is the rate of change for the…
calculating a rate of change of a quadratic function over an interval\nwhat is the rate of change for the interval between 2 and 6 on the x - axis?\n-2\n-1/2\n1/2\n2
Answer
Explanation:
Step1: Recall rate - of - change formula
The rate of change of a function $y = f(x)$ over the interval $[a,b]$ is $\frac{f(b)-f(a)}{b - a}$. Here, $a = 2$ and $b = 6$.
Step2: Determine function values from the graph
From the graph, when $x = 2$, $y=f(2)=2$; when $x = 6$, $y=f(6)=10$.
Step3: Calculate the rate of change
Substitute into the formula: $\frac{f(6)-f(2)}{6 - 2}=\frac{10 - 2}{4}=\frac{8}{4}=2$.
Answer:
2