let $f(x)=x^{2}-2x - 4$. what is the average rate of change for the quadratic function from $x=-1$ to $x =…

let $f(x)=x^{2}-2x - 4$. what is the average rate of change for the quadratic function from $x=-1$ to $x = 4$? enter your answer in the box.

let $f(x)=x^{2}-2x - 4$. what is the average rate of change for the quadratic function from $x=-1$ to $x = 4$? enter your answer in the box.

Answer

Explanation:

Step1: Recall average - rate - of - change formula

The average rate of change of a function $y = f(x)$ from $x=a$ to $x = b$ is $\frac{f(b)-f(a)}{b - a}$. Here, $a=-1$, $b = 4$, and $f(x)=x^{2}-2x - 4$.

Step2: Calculate $f(-1)$

Substitute $x=-1$ into $f(x)$: $f(-1)=(-1)^{2}-2\times(-1)-4=1 + 2-4=-1$.

Step3: Calculate $f(4)$

Substitute $x = 4$ into $f(x)$: $f(4)=4^{2}-2\times4-4=16-8 - 4=4$.

Step4: Calculate the average rate of change

$\frac{f(4)-f(-1)}{4-(-1)}=\frac{4-(-1)}{4 + 1}=\frac{4 + 1}{5}=\frac{5}{5}=1$.

Answer:

$1$