posted by Katlyn on .
I got 2 more intense problems like this. Can someone show me the way for each step so I can follow along with the other problems I have to do? ThankS!
A gardener has 40 feet of fencing with which to enclose a garden adjacent to a long existing wall. The gardener will use the wall for one side and the available fencing for the remaining three sides.
If the sides perpendicular to the wall have length x feet, which of the following (A, B, C, or D) represents the area A of the garden?
A. A(x) = –2x^2 + 20x
B. A(x) = –2x^2 + 40x
C. A(x) = 2x^2 – 40x
D. A(x) = x^2 – 40x
The area function is a quadratic function and so its graph is a parabola.
Does the parabola open up or down?
Find the vertex of the quadratic function A(x). Show work.
Use the work in the previous parts to help determine the dimensions of the garden which yield the maximum area, and state the maximum area. (Fill in the blanks below. Include the units of measurement.)
The maximum area is ______________,
when the sides perpendicular to the wall have length x = ___________
and the side parallel to the wall has length ___________ .
The area is
A(x) = x (40-2x)= -2x^2 + 40x
When plotted vs x, that is an upside down parabola.
Ypu can find the maximum value (apex) with calculus or by completing the square
A = -2(x^2 -20x + 100) +200
= -2(x-10)^2 + 200
The maximum value of A occurs when x=10.
Now you fill in the blanks