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

Question

𝐴
=
−
𝑤
2
+
60
𝑤
, where A
𝐴
is the area and w is the width. Which of the following correctly identifies the x-intercept(s)?(1 point)
Responses

a.(60,0) and (30,900)

b.(0,0) and (60,0)

c.(60,0)

d.(0,0)

Answer 1

To find the x-intercept(s) of the function \( A = -w^2 + 60w \), we need to set the area \( A \) equal to zero and solve for \( w \):

\[ 0 = -w^2 + 60w \]

Rearranging this, we have:

\[ w^2 - 60w = 0 \]

Next, we can factor out \( w \):

\[ w(w - 60) = 0 \]

Setting each factor to zero gives us:

1. \( w = 0 \)
2. \( w - 60 = 0 \) which leads to \( w = 60 \)

Thus, the x-intercepts are \( (0, 0) \) and \( (60, 0) \).

Looking at the provided options, the correct choice that lists these intercepts is:

b. (0, 0) and (60, 0).