Luca is building a garden in his backyard. He needs to erect a fence to keep his dog Luna from digging in it. He has enough materials for a fence with 120 feet around the perimeter. This function is represented by the formula A = -w^2 + 60w, where A is the area and w is the width. Which of the following correctly identifies the x-intercept(s)?
A. (0, 0) and (60, 0)
B. (60, 0)
C. (60, 0) and (30, 900)
D. (0, 0)
The x-intercept(s) of a function are the point(s) where the function intersects the x-axis. In other words, the value(s) of x where the function equals 0.
To find the x-intercept(s) of the function A = -w^2 + 60w, we set A equal to 0 and solve for w:
0 = -w^2 + 60w
Factoring out a w, we get:
0 = w(-w + 60)
So the function intersects the x-axis at w = 0 and -w + 60 = 0.
Solving -w + 60 = 0 for w, we find:
w = 60
Therefore, the correct answer is option B: (60, 0).