To find the x-intercepts of the function \( A = -w^2 + 60w \), we need to set the area \( A \) equal to zero and solve for \( w \):
\[ A = -w^2 + 60w = 0 \]
Factoring the equation gives:
\[ w(-w + 60) = 0 \]
Setting each factor equal to zero gives:
- \( w = 0 \)
- \( -w + 60 = 0 \rightarrow w = 60 \)
Thus, the x-intercepts are \( (0,0) \) and \( (60,0) \).
Therefore, the correct response is:
(0,0) and (60,0)