Writing a Quadratic Model
Lanscape Design
You are putting a stone border along two sides of a rectangular Japanese garden that measures 6 yards by 15 yards. Your budget limits you to only enough stones to cover 46 square yards. How wide should the border be?
Solution
Begin by drawing and labeling a diagram.
Area of Border = Total Area - Garden Area
Write quadratic model.
Multiply
Write in standard form
Factor
or Use zero-product property
Set first factor equal to 0
Solve for x
Set second factor equal to 0
Solve for x
The solutions are and . Only is a reasonable solution, because negative values for dimensions do not make sense. Mark the border 2 yards wide.