for the function ( f(x) = 2x^{2}+4x + 10 ), find the slope of the secant line between ( x=-4 ) and ( x = -2 ).

Question

Accepted Answer

# Explanation:
## Step1: Find $f(-4)$
Substitute $x = -4$ into $f(x)=2x^{2}+4x + 10$.
$$
\begin{align*}
f(-4)&=2\times(-4)^{2}+4\times(-4)+10\
&=2\times16-16 + 10\
&=32-16+10\
&=26
\end{align*}
$$
## Step2: Find $f(-2)$
Substitute $x=-2$ into $f(x)=2x^{2}+4x + 10$.
$$
\begin{align*}
f(-2)&=2\times(-2)^{2}+4\times(-2)+10\
&=2\times4-8 + 10\
&=8-8+10\
&=10
\end{align*}
$$
## Step3: Use the slope formula for the secant line $m=\frac{f(b)-f(a)}{b - a}$
Here $a=-4$, $b = -2$, $f(a)=26$, $f(b)=10$.
$$
\begin{align*}
m&=\frac{f(-2)-f(-4)}{-2-(-4)}\
&=\frac{10 - 26}{-2 + 4}\
&=\frac{-16}{2}\
&=-8
\end{align*}
$$
# Answer:
$-8$

Sovi.AI - AI Math Tutor

QUESTION IMAGE

Question

Explanation:

Step1: Find \(f(-4)\)

Step2: Find \(f(-2)\)

Step3: Use the slope formula for the secant line \(m=\frac{f(b)-f(a)}{b - a}\)

Answer: