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 (60,0) and (30,900) left parenthesis 60 comma 0 right parenthesis and left parenthesis 30 comma 900 right parenthesis (0,0) left parenthesis 0 comma 0 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
1 answer
To find the x-intercepts of the function \( A = -w^2 + 60w \), we need to set the area \( A \) to zero and solve for \( w \):
\[ 0 = -w^2 + 60w \]
Factoring out \( w \):
\[ 0 = w(-w + 60) \]
Setting each factor to zero gives us:
Thus, the x-intercepts are \( (0, 0) \) and \( (60, 0) \).
Among the options given, the correct identification of the x-intercepts is:
(0,0) and (60,0).
