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 domain when the maximum range is achieved?
A. 10 yards
B. 100 yards
C. 10 square yards
D. 5 yards
To find the maximum range of the equation, we need to find the vertex of the equation. The equation is in the form of a quadratic equation, and the vertex of a quadratic equation in the form of A = ax^2 + bx + c is given by the formula x = -b/2a.
In this case, the equation is A = -w^2 + 20w, so the vertex can be found using the formula w = -20/(2*(-1)) = -20/(-2) = 10.
The maximum range is achieved at w = 10, so the domain when the maximum range is achieved is 10 yards. Answer choice A, 10 yards, is the correct answer.