The number of tickets sold each day for an upcoming performance is given by N(x)=-0.5x^2+12x+13, where x is the number of days since the performance was first announced. When will daily ticket sales peak and how many tickets will be sold that day?

Answer 1

It depends a little on what math class you're in how they want you to solve this. But basically, this function is a parabola and you need to find the vertex.
x=-b/(2a), where a=-0.5, and b=12
x=-12/(2*-0.5)=12, this is the x coordinate of the vertex and also the number of days since the performance was announced. Then you substitute 12 in for x in the original equation:
-0.5(12)^2 + 12(12) + 13 = 85. This is the y coordinate of the vertex and the number of tickets sold.
So the daily tickets sales will peak 12 days after the performance was announced, with a maximum of 85 tickets sold that day.