x = 6, x = 44; The zeros represent the number of monthly memberships where no profit is made.
Here we have the function:
[tex]f(x) = -x^2 + 50x - 264[/tex]
that models the profit in dollars, where x is the number of memberships sold. In order to get the zeros we'll use the quadratic formula:
[tex]\quad x_{1,\:2}=\frac{-b\pm \sqrt{b^2-4ac}}{2a} \\ \\ \\ For: \\ \\ a=-1,\:b=50,\:c=-264:\quad x_{1,\:2}=\frac{-50\pm \sqrt{50^2-4\left(-1\right)\left(-264\right)}}{2\left(-1\right)} \\ \\ \\ x_{1}=\frac{-50+\sqrt{50^2-4\left(-1\right)\left(-264\right)}}{2\left(-1\right)}=\frac{-50+\sqrt{50^2-4\cdot \:1\cdot \:264}}{-2\cdot \:1}=\frac{-50+\sqrt{1444}}{-2\cdot \:1}=6 \\ \\ \\[/tex]
[tex]x_{2}=\frac{-50-\sqrt{50^2-4\left(-1\right)\left(-264\right)}}{2\left(-1\right)}=\frac{-50-\sqrt{50^2-4\cdot \:1\cdot \:264}}{-2\cdot \:1}=\frac{-50-\sqrt{1444}}{-2}=44[/tex]
So the zeros are:
[tex]x=6 \\ \\ x=44[/tex]
The zeros occurs when [tex]f(x)=0[/tex], so we can conclude that at those points there is no any profit.
In conclusion:
x = 6, x = 44; The zeros represent the number of monthly memberships where no profit is made.
