A yoga studio sells monthly memberships. The function f(x) = −x2 + 50x − 264 models the profit in dollars, where x is the number

Question

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A yoga studio sells monthly memberships. The function f(x) = −x2 + 50x − 264 models the 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.

x = 6, x = 44; The zeros represent the number of monthly memberships that produces a maximum profit.
x = 6, x = 44; The zeros represent the number of monthly memberships where no profit is made.
x = 25, x = 361; The zeros represent the number of monthly memberships where no profit is made.
x = 25, x = 361; The zeros represent the number of monthly memberships that produces a maximum profit.

Mathematics

2 answers:

-BARSIC- [3] · Answer 1 · 2022-02-12T13:44:46+03:00

<h2>Answer:</h2>

<em>x = 6, x = 44; The zeros represent the number of monthly memberships where no profit is made.</em>

<h2>Explanation:</h2>

Here we have the function:

$f(x) = -x^2 + 50x - 264$

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:

$\quad x_{1,\:2}=\frac{-b\pm \sqrt{b^2-4ac}}{2a} \\ \\ \\ For: \\ \\ a=-1,\:b=50,\:c=-264:\quad x_{1,\:2}=\frac{-50\pm \sqrt{50^2-4\left(-1\right)\left(-264\right)}}{2\left(-1\right)} \\ \\ \\ x_{1}=\frac{-50+\sqrt{50^2-4\left(-1\right)\left(-264\right)}}{2\left(-1\right)}=\frac{-50+\sqrt{50^2-4\cdot \:1\cdot \:264}}{-2\cdot \:1}=\frac{-50+\sqrt{1444}}{-2\cdot \:1}=6 \\ \\ \\$

$x_{2}=\frac{-50-\sqrt{50^2-4\left(-1\right)\left(-264\right)}}{2\left(-1\right)}=\frac{-50-\sqrt{50^2-4\cdot \:1\cdot \:264}}{-2\cdot \:1}=\frac{-50-\sqrt{1444}}{-2}=44$