Question

which is the best estimate for the average rate of change for the quadratic function graph on the interval (0leq xleq4)?
a -2
b -3
c 2
d 3

Explanation:

Step1: Recall the formula for average rate of change

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

Step2: Estimate \(f(0)\) and \(f(4)\) from the graph

Looking at the graph, when \(x = 0\), \(y=f(0)=10\) (approximate value). When \(x = 4\), \(y = f(4)=2\) (approximate value).

Step3: Calculate the average rate of change

Substitute into the formula: \(\frac{f(4)-f(0)}{4 - 0}=\frac{2 - 10}{4}=\frac{-8}{4}=- 2\)

Answer:

A. -2