follow the step - by - step process in parts a through c to determine the difference quotient, $f(x)=2x^{2}+5x - 3$. a. determine $f(x + h)$. $f(x + h)=square$ (simplify your answer. do not factor.) b. simplify the expression $f(x + h)-f(x)$. $f(x + h)-f(x)=square$ (simplify your answer. do not factor.) c. determine the difference quotient $\frac{f(x + h)-f(x)}{h}$.

Question

Accepted Answer

# Explanation:
## Step1: Find f(x + h)
Substitute $x+h$ into $f(x)$:
$$
\begin{align*}
f(x + h)&=2(x + h)^2+5(x + h)-3\
&=2(x^{2}+2xh+h^{2})+5x + 5h-3\
&=2x^{2}+4xh+2h^{2}+5x + 5h-3
\end{align*}
$$
## Step2: Find f(x + h)-f(x)
$$
\begin{align*}
f(x + h)-f(x)&=(2x^{2}+4xh+2h^{2}+5x + 5h-3)-(2x^{2}+5x - 3)\
&=2x^{2}+4xh+2h^{2}+5x + 5h-3 - 2x^{2}-5x + 3\
&=4xh+2h^{2}+5h
\end{align*}
$$
## Step3: Find the difference quotient $\frac{f(x + h)-f(x)}{h}$
$$
\begin{align*}
\frac{f(x + h)-f(x)}{h}&=\frac{4xh+2h^{2}+5h}{h}\
&=\frac{h(4x + 2h+5)}{h}\
&=4x+2h + 5
\end{align*}
$$
# Answer:
a. $2x^{2}+4xh+2h^{2}+5x + 5h-3$
b. $4xh+2h^{2}+5h$
c. $4x+2h + 5$

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QUESTION IMAGE

Question

Explanation:

Step1: Find f(x + h)

Step2: Find f(x + h)-f(x)

Step3: Find the difference quotient \(\frac{f(x + h)-f(x)}{h}\)

Answer: