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

Question

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
(60,0)
left parenthesis 60 comma 0 right parenthesis
(0,0)
and (60,0)

Answer 1

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

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

Factoring the quadratic equation:

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

This gives us two solutions:

\[ w = 0 \quad \text{or} \quad -w + 60 = 0 \implies w = 60 \]

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

The correct option that identifies the x-intercepts is:

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