Pearson Algebra 2 Common Core, 2011
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Pearson Algebra 2 Common Core, 2011 View details
2. Standard Form of a Quadratic Function
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Exercise 38 Page 207

Notice that one side of the playground does not require fencing.

Practice makes perfect

Let's define a variable for each dimension of the rectangle. Let be the width and be the length.

The perimeter of a rectangle is but one side does not require fencing. This means the perimeter of the playground is Since there is of fence, then which means that

Now, we can write the area of the rectangular playground.
This is a quadratic function that models the area of the playground. Let's rewrite it in standard form.
Let's identify the coefficients of the above quadratic function. As we can see and Since is a negative number the parabola opens downward, which implies that its maximum point corresponds to the vertex. Let's find the coordinate of the vertex.
Let's simplify above quotient to calculate
Simplify right-hand side
The length that maximizes the area of the playground is To know what is the greatest area, we must find
Simplify right-hand side
Consequently, the greatest area we can fence is