Question

use a quadratic function to model the area of the rectangle. graph the function.
the function is f(x)=\square
(simplify your answer.)

Explanation:

Step1: Recall area of rectangle formula

The area \( A \) of a rectangle is given by the product of its length and width. Here, the length is \( 2x + 2 \) and the width is \( x + 4 \), so the area function \( f(x)=(2x + 2)(x + 4) \).

Step2: Expand the product

Using the distributive property (FOIL method):
\[

$$\begin{align*} (2x + 2)(x + 4)&=2x\cdot x+2x\cdot 4+2\cdot x+2\cdot 4\\ &=2x^{2}+8x + 2x+8\\ &=2x^{2}+10x + 8 \end{align*}$$

\]

Answer:

\( 2x^{2}+10x + 8 \)