Question

Use the expressions that represent the length and width of the game board to write an equation that models the area of the figure. Let y represent the area, and write your answer in the form y=ax^2+bx+c, where a,b, and c are real numbers.

Answer 1

The picture is incomplete and the width is missing.

I am going to show you how to do it using any width.

The length shown is x + 4 and the width starts with - x.

Assume the width is - x + a.

Then the area of the rectangle with dimensions x + 4 and - x + a is calculated in this way:

1) given: (x + 4) (- x + a)

2) use distribuitive property: (x)(-x) + (x)(a) + (4)(-x) + (4)(a)

= - x^2 +ax -4x + 4a

3) Combine like terms: - x^2 + (a -4)x + 4a

If the polynomial missing were - x + 7, the answer would be:

- x^2 + (7 -4)x + 4(7) = - x^2 + 3x + 28

With this you are able to get the answer using the real values.