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. Thisfunction is represented by the formula A = -w^2 + 60w, where A is the area and wis the
width. Which of the following correctly identifies the x-intercepts)? (1 point)
(0,0)
(60, 0)
(0, 0) and (60, 0)
(60, 0) and (30, 900)

Answer 1

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

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

We can factor this equation:

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

Setting each factor equal to zero gives us the x-intercepts:

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

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

The correct identification of the x-intercepts is:

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