SOLUTION: problem solving using quadratic functions:
Philip wants to construct a dog pen at the back of his garage. He will use the wall of the garage as one side of the pen and will con
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Question 1122449: problem solving using quadratic functions:
Philip wants to construct a dog pen at the back of his garage. He will use the wall of the garage as one side of the pen and will construct the rest of the rectangular pen from 28 yards of fencing. What should the dimensions of the pen be if Philip wants it to have maximum area.
Part 2
Rework part 1 this time assuming the garage abuts the rear of the property and a neighbor was permitted to attach 6 feet of fencing to it.Use this section of fence as well as the side of the garage as part of the pen.
Answer by solver91311(24713) (Show Source): You can put this solution on YOUR website!
Area as a function of rectangle width:
\ =\ -2w^2\ +\ 28w)
This is a quadratic function with a negative lead coefficient, hence the graph is a parabola that opens downward. That means that the vertex of the parabola represents a maximum area. To find the dimensions of the maximum area rectangle, calculate the abscissa of the vertex, namely the value of 
at the vertex, then calculate 
.
Hint: the vertex of a parabola with equation \ =\ ax^2\ +\ bx\ +\ c)
is at the point \))
John
My calculator said it, I believe it, that settles it
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