Pam is installing a new window in her backyard workshop, to let in more natural light. She wants the window to be square, since she thinks that will look best, and she will include a $1.5$ -inch-wide window frame on all four sides of the window. $\newline$ The total area of the window and frame in square inches can be modeled by the expression $(x + 3)(x + 3)$ , where $x$ is the width of the window in inches. This expression can also be written in the form $x^2 + 6x + 9$ . $\newline$ What does the quantity $6x + 9$ represent in the expression? $\newline$ Choices: $\newline$ (A)the perimeter around the outside of the frame in inches $\newline$ (B)the width of the window and frame together in inches $\newline$ (C)the area of the frame in square inches $\newline$ (D)the area of the window in square inches $\newline$

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Algebra 2

Interpret parts of quadratic expressions: word problems

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Q. Pam is installing a new window in her backyard workshop, to let in more natural light. She wants the window to be square, since she thinks that will look best, and she will include a

1.5

-inch-wide window frame on all four sides of the window.

\newline

The total area of the window and frame in square inches can be modeled by the expression

(x + 3)(x + 3)

, where

x

is the width of the window in inches. This expression can also be written in the form

x^2 + 6x + 9

\newline

What does the quantity

6x + 9

represent in the expression?

\newline

Choices:

\newline

(A)the perimeter around the outside of the frame in inches

\newline

(B)the width of the window and frame together in inches

\newline

(C)the area of the frame in square inches

\newline

(D)the area of the window in square inches

\newline

Total Area Expression: The expression for the total area is $(x + 3)(x + 3)$ , which is the same as $x^2 + 6x + 9$ .
Window and Frame Width: $x$ represents the width of the window, so $x + 3$ represents the width of the window plus the frame on one side.
Additional Frame Width: Since the frame is $1.5$ inches wide on all four sides, the total additional width added by the frame is $1.5$ inches times $2$ , which equals $3$ inches.
Area of Frame: The term $6x$ represents twice the product of the width of the window and the width added by the frame, which is part of the area of the frame.
Area of Frame's Corners: The constant $9$ represents the area of the frame's corners, which is $1.5$ inches by $1.5$ inches on each of the four corners, so $1.5 \times 1.5 \times 4$ equals $9$ .