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)?(1 point) Responses (60,0) and (30,900) left parenthesis 60 comma 0 right parenthesis and left parenthesis 30 comma 900 right parenthesis (0,0) and (60,0) left parenthesis 0 comma 0 right parenthesis and left parenthesis 60 comma 0 right parenthesis (60,0) left parenthesis 60 comma 0 right parenthesis (0,0) left parenthesis 0 comma 0 right parenthesis
To find the x-intercepts, we need to set A (the area) to 0 and solve for w.
So, we have the equation:
0 = -w^2 + 60w
Setting the equation equal to 0, we get:
w^2 - 60w = 0
Factoring out w, we have:
w(w - 60) = 0
Setting each factor equal to 0, we find two possible solutions:
w = 0 or w - 60 = 0
The first solution, w = 0, represents the x-intercept at (0, 0).
The second solution, w - 60 = 0, gives us w = 60, which represents the x-intercept at (60, 0).
Therefore, the correct answer is (0, 0) and (60, 0).