<PRE><B>Question 1132198</B>
the graph is shown below:


&lt;img src = &quot;http://theo.x10hosting.com/2018/123001.jpg&quot; alt=&quot;$$$&quot; &gt;


x represents the price of a ticket.
y represents the income.


from the graph, it can be seen that:


when the cost of a ticket is 0 dollars, they will lose 44 dollars.
when the cost of a ticket is 2 dollars, they will break even.
when the cost of a ticket is 12 dollars, they will make 100 dollars.
when the cost of a ticket is 22 dollars, they will break even.
when the cost of a ticket is 24 dollars, they will lose 44 dollars.


answers to the questions are shown below:


a)draw the graph of income versus the cost of a ticket.
done - see above.
b)Determine the minimum cost of a ticket for the theater club to break even.
2 dollars
c)Determine the maximum cost of a ticket that the theater club can charge and break even.
22 dollars
d)How much should they charge to receive maximum income?
12 dollars
e)Find the maximum income.
100 dollars


the break even income can also be found by factoring the quadratic equation.
the maximum income can also be found by finding the value of x = -b/2a and then evaluating the equation with that value of x.


the equation is y = -x^2 + 24x - 44.
to factor, do the following:
set y equal to 0 to get -x^2 + 24x - 44 = 0
multiply both sides by -1 to get (-1) * (x^2 - 24x + 44) = 0
factor x^2 - 24x + 44 to get (x - 2) * (x - 22)
the equation becomes (-1) * (x - 2) * (x - 22) = 0
the equation will be equal to 0 when x = 2 or when x = 22 or when x = 2 and x = 22.


to find the maximum income, do the following:
place the equation in standaed form of y = -x^2 + 24x - 44
when in this form:
a = coefficient of the x^2 term = -1
b = coefficient of the x term = + 24
c = constant term = -44
the maximum income will be at x = -b/2a = -24/-2 = 12
the maximum income will be -12^2 + 24*12 - 44 = 100


note that -12^2 is equal to - (12^2) and not equal to (-12)^2.
the value that&#39;s being square is the 12, not the -12.


the graph confirms that the maximum value is at x = 12.
the graph confirms that the income is 0 when x = 2 and when x = 22.
the graph confirms that the school loses 44 dollars when x = 0 and when x = 24.









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