Answer:
Area A = -x² + x + 72
Explanation:
Area of a rectangle = L x W where L = length and W = width
Originally L = 9 feet, W = 8 feet
Area A = 72 sq ft
When L is decreased by x feet, W is increased by x feet.
So,
new L = 9 - x
new W = 8 + x
new A = (9 - x)(8 + x)
Using FOIL method we evaluate the above expression as:
= (9)(8) + 9x - 8x - x²
= 72 + x - x²
This is a quadratic expression which in standard form is given by
A = -x² + x + 72
(arranged highest to lowest power terms but does not really affect the meaning or result of the expression)