find the average rate of change of $g(x)=x^{2}-5x + 2$ from $x = 2$ to $x = 5$. simplify your answer as much…

Explanation:

Step1: Recall average - rate - of - change formula

The average rate of change of a function $y = g(x)$ from $x = a$ to $x = b$ is $\frac{g(b)-g(a)}{b - a}$. Here, $a = 2$, $b = 5$, and $g(x)=x^{2}-5x + 2$.

Step2: Calculate $g(5)$

Substitute $x = 5$ into $g(x)$: $g(5)=5^{2}-5\times5 + 2=25-25 + 2=2$.

Step3: Calculate $g(2)$

Substitute $x = 2$ into $g(x)$: $g(2)=2^{2}-5\times2 + 2=4-10 + 2=-4$.

Step4: Calculate the average rate of change

$\frac{g(5)-g(2)}{5 - 2}=\frac{2-(-4)}{3}=\frac{2 + 4}{3}=\frac{6}{3}=2$.

Answer:

$2$