Nora is creating a dog run in her backyard for her dog, Max. She has enough materials to create a run with a perimeter of 120 feet. This is represented by the function A=−w2+60w

Question

where A
is the area of the run and w is the width. Which of the following identifies the x-intercept(s)?(1 point)
Responses

(30,900)
and (60,0)
left parenthesis 30 comma 900 right parenthesis and left parenthesis 60 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

(0,0)

Answer 1

To find the x-intercepts of the function \( A = -w^2 + 60w \), we need to set \( A \) to 0 and solve for \( w \):

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

Rearranging gives us:

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

We can factor the equation:

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

Setting each factor to zero gives us the solution for \( w \):

1. \( w = 0 \)
2. \( w - 60 = 0 \) → \( w = 60 \)

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

Among the provided responses, the correct identification of the x-intercepts is:

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