Question

Now describe a situation involving area in square feet that can be modeled using the function g(x) = 2x2 − 13x + 6 so that it relates to last situation you came up with.

Answer 1

Based on the situation in part A, the width of a rectangular garden is x feet, and its length is 5 feet more than twice its width. The right side of the equation, g(x) = 2x2 − 13x + 6, can be factored to g(x) = (2x − 1)(x − 6). This function could represent an inner region of the garden from the first equation, such as a vegetable garden with a border around it. The length of this inner garden would be 2x − 1 feet, and the width would be x − 6, which would leave a 3-foot border around the garden.

Explanation:

Edmentum explanation/answer

Answer 2

`Length = 2x - 1`

`Width = x - 6`

Explanation:

Given

`g(x) = 2x^2 - 13x + 6`

Required

Model as the area

`g(x) = 2x^2 - 13x + 6`

Expand:

`g(x) = 2x^2 - 12x -x+ 6`

Factorize:

`g(x) = 2x(x - 6) -1(x- 6)`

`g(x) = (2x - 1) (x- 6)`

Area is calculated as:

`Area = Length * Width`

So, by comparison:

`Length = 2x - 1`

`Width = x - 6`