for the function $f(x)=-2x^{2}-4x + 6$, find the slope of the secant line between $x=-1$ and $x = 2$.

Question

Accepted Answer

# Explanation:
## Step1: Find $f(-1)$
Substitute $x = -1$ into $f(x)=-2x^{2}-4x + 6$.
$$
\begin{align*}
f(-1)&=-2\times(-1)^{2}-4\times(-1)+6\
&=-2\times1 + 4+6\
&=-2 + 4+6\
&=8
\end{align*}
$$
## Step2: Find $f(2)$
Substitute $x = 2$ into $f(x)=-2x^{2}-4x + 6$.
$$
\begin{align*}
f(2)&=-2\times2^{2}-4\times2+6\
&=-2\times4-8 + 6\
&=-8-8 + 6\
&=-10
\end{align*}
$$
## Step3: Calculate the slope of the secant line
The slope formula of the secant line between two points $(x_1,y_1)$ and $(x_2,y_2)$ is $m=\frac{y_2 - y_1}{x_2 - x_1}$. Here $x_1=-1,y_1 = f(-1)=8,x_2 = 2,y_2=f(2)=-10$.
$$
\begin{align*}
m&=\frac{f(2)-f(-1)}{2-(-1)}\
&=\frac{-10 - 8}{2 + 1}\
&=\frac{-18}{3}\
&=-6
\end{align*}
$$
# Answer:
$-6$

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QUESTION IMAGE

Question

Explanation:

Step1: Find \(f(-1)\)

Step2: Find \(f(2)\)

Step3: Calculate the slope of the secant line

Answer: