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Sagot :
The zeros represent the number of monthly memberships where no profit is made; x = 6, x = 44.
To determine the zeroes, calculate:
The function we have is: [tex]f(x) = -x^{2} +50x-264[/tex]
That models the profit in dollars, where [tex]x[/tex] is the number of memberships sold.
In order to get the zeros we'll use the quadratic formula:
[tex]x_{1,2} =\frac{-b+-(b^{2}-4ac) }{2a} \\[/tex]
For,
[tex]a=-1,b=50,c=-264: x^{1,2} =\frac{-50+-\sqrt[]{50^{2} -4(-1)(-264)} }{2(-1)} \\x_{1} =\frac{-50+\sqrt[]{50^{2} -4(-1)(-264)} }{2(-1)} =\frac{-50+\sqrt[]{50^{2} -4*1*264} }{2(-1)}=\frac{-50+\sqrt[]{1444} }{-2} =6\\x_{2} =\frac{-50+\sqrt[]{50^{2} -4(-1)(-264)} }{2(-1)} =\frac{-50-\sqrt[]{50^{2} -4*1*264} }{2(-1)}=\frac{-50-\sqrt[]{1444} }{-2} =44\\[/tex]
So, the zeroes are [tex]x=6, x=44[/tex].
Therefore, the zeros represent the number of monthly memberships where no profit is made; x = 6, x = 44.
Know more about a function here:
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The complete question is given below:
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 produce 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 produce a maximum profit.
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