Miss bell decorates her gazebo with colored lights. The base of the gazebo is a circle with a diameter of 12 feet. Using the same length of lights she's going to decorate the side of her garden shed which has a square base. What is the maximum side length of the shed

The maximum side length of the shed = 9.42 ft

Step-by-step explanation:

From the given information:

Miss bell decorates her gazebo with coloured lights who base is a circle with diameter 12 feet. The first find the circumference of the gazebo by using the circumference of a circle since the base takes such shape.

Circumference of a circle = πd

Circumference of a circle = π × 12

Circumference of a circle = 37.699

Then; the circumference of the circle equates to the length of the lights.

However, using the same length, the maximum side length of the  garden shed whose base took a square form can be determined by using the perimeter of a square as the square length, which is;

P = 4L

where;

L = length of sides

37.699 = 4L

L = 37.699/4

L = 9.42 ft

Thus, the maximum side length of the shed = 9.42 ft

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let's cover over the formula of the vertex:

y = a(x – h)^2 + k

in this formula, (h,k) are the vertex, always remember that the positive or negative value of the vertex is based on the sign it has.

for example, if the vertex is -3,-6 then both the x and y value would have the positive sign attached to it and if it were a positive x and y value, then a negative sign would be attached to it.

with that being said, for our problem the x value is a positive one so we are looking for a number with a negative sign next to it, in this case the first and second choice.

however, for the first answer choice it isn't quite part of the formula so we know that the answer choice correctly displays the x value.

to confirm, we can see if the -1 fits correctly with the second answer choice, and as mentioned above a negative number will have a positive sign attached to it. so, for our problem we can see that -1 has been changed to +1, so we can confirm that the second answer choice is correct.

hence, our final answer is y=(x - 1)^2 + 1