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Chapter 6: Q50. (page 292)

Steve has 120 feet of fence to make a rectangular kennel for his dogs. He will use his house as one side. Find the maximum area of the kennel.

Short Answer

Expert verified

The maximum area of kennel is 1800ft2.

Step by step solution

01

Step 1. Given Information.

Steve has 120 feet of fence. He uses his house as one side.

Let

w = width of house

l = length of kennel

02

Step 2. Use the concept.

The y-intercept is the point where the graph intersects they-axis.

Consider the function f(x)=ax2+bx+c,a鈮�0, the x-coordinate of vertex is -b2a.

The graph of f(x)=ax2+bx+c,a鈮�0

  • opens up and has a minimum value when a>0, and
  • opens down and has a maximum value when a<0
03

Step 3. Solution.

The dimensions that produce maximum area should be 30 ft and 60 ft.

So, the maximum area of kennel is

Area=length鈰�width鈬�A=30鈰�60鈬�A=1800ft2

So, the maximum area of kennel is 1800ft2

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Most popular questions from this chapter

Complete parts a-c for each quadratic function.

a. Find y-intercept, the equation of the axis of symmetry, and the x-coordinate of the vertex.

b. Make a table of values that includes the vertex.

c. Use this information to graph the function.

f(x)=-0.25x2-3x

Complete parts a-c for each quadratic function.

  1. Find y-intercept, the equation of the axis of symmetry, and the x-coordinate of the vertex.
  2. Make a table of values that includes the vertex.
  3. Use this information to graph the function.

f(x)=2x2

A tour bus in the historic district of Savannah, Georgia, serves 300 customers a day. The charge is \(8 per person. The owner estimates that the company would lose 20 passengers a day for each \)1 fare increase. What charge would give the most income for the company?

Steve has 120 feet of fence to make a rectangular kennel for his dogs. He will use his house as one side. Write an algebraic expression for the kennel鈥檚 length.

Complete parts a-c for each quadratic function.

  1. Find y-intercept, the equation of the axis of symmetry, and the x-coordinate of the vertex.
  2. Make a table of values that includes the vertex.
  3. Use this information to graph the function.

f(x)=x2-4x-5
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