Marilee is creating a garden in her yard. She needs to put up a fence to keep the animals out of it. She has 40 yards of fencing she can erect. This situation is modeled using the equation A = −w^2 + 20w , where A is the area of the fence and w is the width of the fence. Using the equation, what is the domain when the maximum range is achieved? (1 point) Responses 10 yards 10 yards 10 square yards 10 square yards 5 yards 5 yards 100 yards 100 yards
To find the domain when the maximum range is achieved, we need to find the maximum value of the function A = -w^2 + 20w.
To find the maximum value of a quadratic function, we can use the vertex formula. The x-coordinate of the vertex of a quadratic function in the form f(x) = ax^2 + bx + c is given by x = -b/2a.
In this case, the equation A = -w^2 + 20w is already in the form of a quadratic function, where a = -1, b = 20, and c = 0. So the x-coordinate of the vertex is w = -20/(2*-1) = 10.
Therefore, the maximum range is achieved when the width of the fence is 10 yards.