You have 300 feet of fence. You need to build a garden, where 3 walls are fence and the 4th wall is your house. What is the maximum area of the garden you can make with 300 feet of fence?
let the single side be y ft, the two equal sides be x
2x + y = 300
y = 300-2x
area = xy = x(300-x)
= -2x^2 + 300x
you want the vertex of this downwards parabola
the x of the vertex is -b/(2a) = -300/-4 = 75
y = 300-150 = 150
max area = xy = 75(150) = 11250 ft^2