Question

use a quadratic function to model the area of the rectangle. graph the function.
3x + 9
x + 1
the function is f(x) =
(simplify your answer.)

Explanation:

Step1: Recall area formula for rectangle

The area \( A \) of a rectangle is given by the product of its length and width. Here, the length is \( 3x + 9 \) and the width is \( x + 1 \). So, the area function \( f(x) \) is the product of these two expressions: \( f(x)=(3x + 9)(x + 1) \).

Step2: Expand the product

Using the distributive property (FOIL method), we multiply each term in the first binomial by each term in the second binomial:
\[

$$\begin{align*} (3x + 9)(x + 1)&=3x\cdot x+3x\cdot1 + 9\cdot x+9\cdot1\\ &=3x^{2}+3x + 9x+9\\ &=3x^{2}+12x + 9 \end{align*}$$

\]

Answer:

\( 3x^{2}+12x + 9 \)