Question

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 = -w? + 60w, where A is the area of the run and wis the width. Which of the
following best analyzes the meaning of the x-intercept? (1 point)
• The dog run must have a width between 0 and 900 feet.
• The dog run must have a width between 0 and 30 feet.
• The dog run must have a width between 0 and 60 feet.
• The dog run must have a width between 0 and 120 feet.

Answer 1

A = -w^2 + 60w = w(60 − w), so the x-intercepts are w = 0 and w = 60. Those are the widths that make the area zero (zero width or zero length), and the area is positive only for 0 < w < 60.

So the correct choice is: The dog run must have a width between 0 and 60 feet.