A company offers rectangular pool sizes with the dimensions shown. Each pool includes a deck around it. Write a quadratic function to represent the area of the pool and the deck. If Carolina wants a 15 foot pool with a deck, how many square feet will she need ot have available in her yard?

The area of the quadratic function that represents the area of the pool is 2x² ft²
The area of the quadratic function that represents the area of the pool with deck is (2x²+90x+900) ft²

The formula for calculating the area of a rectangle is expressed as:

A = LW where

L is the length

W is the width

For the pool

Length = 2x

With = x

Get the equation for the area.

Area = 2x * x

Area = 2x²

Hence the area of the quadratic function that represents the area of the pool is 2x² ft²

For the pool with deck

length = 15 + 2x + 15 = 30+2x

Width = 15 + x + 15 = 30+x

Get the areas of the pool with deck

A 60x+2x= (30+2x)(30+x)

A = 900+30x+60x+2x²

A = 2x²+90x+900

The area of the quadratic function that represents the area of the pool with deck is (2x²+90x+900) ft²

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