what is the average rate of change for this quadratic function for the interval from x = 1 to x = 3?

Answer:

-2

Explanation:

Step1: Recall average - rate - of - change formula

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, $a = 1$, $b = 3$.

Step2: Estimate function values from graph

From the graph, when $x = 1$, assume $y_1=f(1)= - 3$ (by estimating the $y$ - value at $x = 1$). When $x = 3$, assume $y_2=f(3)= - 7$ (by estimating the $y$ - value at $x = 3$).

Step3: Calculate average rate of change

Substitute into the formula: $\frac{f(3)-f(1)}{3 - 1}=\frac{-7-( - 3)}{2}=\frac{-7 + 3}{2}=\frac{-4}{2}=-2$.