Question

A bookstore's monthly earnings may be modeled by the function f(x)=−3x2+12x+180
, where f(x)
represents the amount of money the bookstore earns in a month and x
represents the number of months that have passed since the bookstore opened.

Which statements are true? Select three that apply.

(3 points)
Responses

The most money the bookstore will earn during one of the months is $192.
The most money the bookstore will earn during one of the months is $192.

The only reasonable zero in this context is x=6
.
The only reasonable zero in this context is x is equal to 6.

The only reasonable zero in this context is x=180
.
The only reasonable zero in this context is x is equal to 180.

The zeros of the function represent the months in which the bookstore earned $0.
The zeros of the function represent the months in which the bookstore earned $0.

The only reasonable zero in this context is x=10
.
The only reasonable zero in this context is x is equal to 10.

The most money the bookstore will earn during one of the months is $180.

Answer 1

True statements (with brief reasons):

1. The most money the bookstore will earn during one of the months is $192.
- Vertex at x = -b/(2a) = 2; f(2) = -3(2)^2 + 12(2) + 180 = 192.

2. The only reasonable zero in this context is x = 10.
- Solve -3x^2 + 12x + 180 = 0 → x = 10 or x = -6; x = -6 is not reasonable (negative months).

3. The zeros of the function represent the months in which the bookstore earned $0.
- Zeros satisfy f(x) = 0, so they correspond to months with $0 earnings.