SOLUTION: If 800 feet of fence are used to enclose a rectangular pen, the resulting area of the pen is A(x)=x(400-x), where x is the width of the pen. Is A(x) a quadratic function? What is t

Question 1152698: If 800 feet of fence are used to enclose a rectangular pen, the resulting area of the pen is A(x)=x(400-x), where x is the width of the pen. Is A(x) a quadratic function? What is the maximum area of the pen? What are the dimensions of the maximum pen?
Found 2 solutions by josgarithmetic, ikleyn:
Answer by josgarithmetic(39613)   (Show Source): You can put this solution on YOUR website!
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A(x)=x(400-x), where x is the width of the pen. Is A(x) a quadratic function?
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Obviously yes.

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What is the maximum area of the pen?
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roots 0 and 400, exact middle being 200 for x.
Maximum area

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What are the dimensions of the maximum pen?
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Look again; you can already see this.
Answer by ikleyn(52750)   (Show Source): You can put this solution on YOUR website!
.

See the lessons
    - HOW TO complete the square to find the minimum/maximum of a quadratic function
    - Briefly on finding the minimum/maximum of a quadratic function
    - HOW TO complete the square to find the vertex of a parabola
    - Briefly on finding the vertex of a parabola
    - A rectangle with a given perimeter which has the maximal area is a square
    - A farmer planning to fence a rectangular garden to enclose the maximal area
in this site, where similar problems were solved and explained in all details.

Also, you have this free of charge online textbook in ALGEBRA-I in this site
    - ALGEBRA-I - YOUR ONLINE TEXTBOOK.

The referred lessons are the part of this textbook under the topic "Finding minimum/maximum of quadratic functions".

Save the link to this online textbook together with its description

Free of charge online textbook in ALGEBRA-I
https://www.algebra.com/algebra/homework/quadratic/lessons/ALGEBRA-I-YOUR-ONLINE-TEXTBOOK.lesson

to your archive and use it when it is needed.

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