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)
left parenthesis 0 comma 0 right parenthesis
(60,0)
left parenthesis 60 comma 0 right parenthesis
(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
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To find the x-intercept(s), we need to set A (the area) equal to 0 and solve for w (the width).
A = -w^2 + 60w
Setting A = 0:
0 = -w^2 + 60w
Factoring out a -w:
0 = w(-w + 60)
Setting each factor equal to 0:
w = 0 or -w + 60 = 0
Simplifying the second equation:
-w + 60 = 0
w = 60
Therefore, the x-intercepts are w = 0 and w = 60.
The correct answer is (0,0) and (60,0).