Question

Zeke wants to build a fence around his backyard with the 200 feet (ft) of fencing he bought at Lowe's. Zeke wants to use all of the fencing he bought. he also wants the length of the fencing to be 10 times the width. the equation A=200w-10w^2 can be used to find the area of the garden, where w is the width of the garden, in ft​

Answer 1

Considering the vertex of the quadratic equation, the width that will maximize the area of the garden, and the maximum area, are as follows:

• Width: 10 ft.

• Maximum area: 1000 ft².

What is the vertex of a quadratic equation?

A quadratic equation is defined as follows:

y = ax² + bx + c.

The vertex can be either a maximum point or a minimum point, depending on the coefficient a, as follows:

• Maximum: a < 0.

• Minimum: a > 0.

The coordinates of the vertex are given as follows:

• x = -b/2a.

• y = -(b² - 4ac)/4a.

For this problem, the equation is:

A(w) = -10w² + 200w.

Hence the coefficients are:

a = -10, b = 200, c = 0.

The width that will maximize the area is:

w = -200/(2(-10)) = 200/20 = 10 ft.

The maximum area is of:

A = -(200)²/(4(-10)) = 1000 ft².

Missing Information

The problem is incomplete and could not be found on any search engine, hence we suppose that it asks for the width that will maximize the area of the garden, and the maximum area.

More can be learned about the vertex of the quadratic equation at brainly.com/question/24737967

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