Question

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)
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)

Answer 1

Set A = 0: −w^2 + 60w = 0 → w(60 − w) = 0, so w = 0 or w = 60.
Thus the x-intercepts are (0, 0) and (60, 0).