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=−w2+60w , where A is the area and w is the width. Which of the following correctly identifies the x-intercept(s)?(1 point)
Responses
(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
(60,0) and (30,900)
To find the x-intercepts of the equation A = -w^2 + 60w, we set A = 0 and solve for w:
-w^2 + 60w = 0
Factoring out w:
w(-w + 60) = 0
Setting each factor equal to zero:
w = 0, or -w + 60 = 0
Solving the second equation:
-w + 60 = 0
-w = -60
w = 60
Therefore, the x-intercept(s) are (0,0) and (60,0).
The correct response is: (0,0) and (60,0)