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
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
(60,0)
left parenthesis 60 comma 0 right parenthesis
(30,900)
and (60,0)
left parenthesis 30 comma 900 right parenthesis and left parenthesis 60 comma 0 right parenthesis
(0,0)
left parenthesis 0 comma 0 right parenthesis
(0,0)
and (60,0)
To find the x-intercepts for the function A = -w^2 + 60w, we need to find the values for w where the area A is zero.
Setting A to zero, we get:
0 = -w^2 + 60w
This quadratic equation can be factored as follows:
0 = w(-w + 60)
Setting each factor equal to zero gives us the solutions for w:
w = 0 or -w + 60 = 0 => w = 60
So, the x-intercepts (where the area is zero, which would be the points where the width of the dog run would be zero, making the area zero) are at w = 0 and w = 60. Since x-intercepts are normally presented as points on a Cartesian plane where y (or A in this function) is zero, the x-intercepts would be:
(0,0) and (60,0)
Hence, the correct answer is:
(0,0) and (60,0)