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?
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.
To determine when daily ticket sales will peak and how many tickets will be sold on that day, we need to find the vertex of the quadratic function N(x).
The vertex of a quadratic function in the form of y = ax^2 + bx + c is given by the formula:
x = -b / (2a)
In this case, the equation for daily ticket sales is N(x) = -0.5x^2 + 12x + 13, so a = -0.5 and b = 12.
Substituting these values into the formula, we get:
x = -12 / (2 * -0.5)
x = -12 / -1
x = 12
The x-coordinate of the vertex is 12. Now, to find the number of tickets sold on that day, we substitute this x-coordinate into the quadratic function.
N(12) = -0.5(12)^2 + 12(12) + 13
N(12) = -0.5(144) + 144 + 13
N(12) = -72 + 144 + 13
N(12) = 85
Therefore, the daily ticket sales will peak on the 12th day, and 85 tickets will be sold on that day.