To find the maximum area of the fence, we need to find the vertex of the quadratic equation. The formula to find the x-value of the vertex of a quadratic equation in the form A = ax^2 + bx + c is x = -b/(2a).
In this case, the equation is A = -w^2 + 60w.
Comparing this to the form A = ax^2 + bx + c, we have:
a = -1
b = 60
Using the formula x = -b/(2a), we can find the x-value of the vertex:
x = -60/(2 * -1)
x = -60/-2
x = 30
Now we can substitute this x-value back into the equation to find the maximum area:
A = -(30)^2 + 60(30)
A = -900 + 1800
A = 900
Therefore, the maximum area the fence can have is 900 square feet.
Nora is creating a dog run for her dog, Mr. Darcey. She has enough fencing material for a fence with a perimeter of 120 feet. This situation is modeled using the equation A=−w2+60w%0D%0A%0D%0A=%0D%0A−%0D%0A%0D%0A2%0D%0A+%0D%0A60%0D%0A%0D%0A where A%0D%0A%0D%0A is the area and w is the width. Using this equation, identify the maximum range or area the fence can have.
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