Question

A local gym sells monthly memberships. The function f(x) = −x2 + 18x − 72 models the daily profit in dollars, where x is the number of memberships sold.

Determine the zeros, and explain what these values mean in the context of the problem. (1 point)

x = 9, x = 18; The zeros represent the number of monthly memberships that produces a maximum profit.

x = 9, x = 18; The zeros represent the number of monthly memberships where no profit is made.

x = 6, x = 12; The zeros represent the number of monthly memberships that produces a maximum profit.

x = 6, x = 12; The zeros represent the number of monthly memberships where no profit is made.

Answer 1

First, allow this to guide you and memorize it:

Answer 2

Factor the equation. Remember, find a common multiple.

Answer 3

The zeros are values of x that make the equation zero. It is where the graph of the model, or function, touches the x-axis. As we can see, the zeros are 6 and 12. Anything negative in this model means a loss in money and we cannot have negative x (members). Due to the curve of this model, if we look at the graph, the zero on the left is the least number of members to break even and from there until you get to the zero on the right is profits. When the point on the right you get back to the breakeven point before the profit is negative.

Answer 4

So, the "breakeven" point I am referring to is the point where no profits are made, where y = 0, and so the solution should be the final option. If you want to know some useful tools in math, I have used Desmos and Symbolab which are online and free to use. There are many other very useful sites related to math which I will list here:
d26tpo4cm8sb6k.cloudfront (dot) net
Mathway
Geogebra
ChristopherChudzicki.github (dot) io
WolframAlpha
Interactive Mathematics
Some of them can help you calculate things in chemistry, finances, and even fitness & health.