Question

use a quadratic function to model the area of the rectangle. graph the function.
2x + 6
x + 1
the function is f(x) = \square.
(simplify your answer.)

Explanation:

Step1: Recall rectangle area formula

Area = length $\times$ width

Step2: Substitute given expressions

$f(x)=(2x+6)(x+1)$

Step3: Expand using distributive property

$f(x)=2x(x+1)+6(x+1)$
$f(x)=2x^2+2x+6x+6$

Step4: Combine like terms

$f(x)=2x^2+(2x+6x)+6$
$f(x)=2x^2+8x+6$

Answer:

$f(x)=2x^2+8x+6$