Suppose you are an event coordinator for a large performance theater. One of the hottest new Broadway musicals has started to tour, and your city is the first stop on the tour. You need to supply information about projected ticket sales to the box office manager. The box office manager uses this information to anticipate staffing needs until the tickets sell out. You provide the manager with a quadratic equation that models the expected number of ticket sales for each day x. ( is the day tickets go on sale).


. Use the quadratic equation to determine the last day that tickets will be sold. (Note: Write your answer in terms of the number of days after ticket sales begin.)

Use the quadratic equation to determine the last day that tickets will be sold. (Note: Write your answer in terms of the number of days after ticket sales begin.)

tickets=-0.2x^2+12x+11

Use the quadratic equation to determine the last day that tickets will be sold. (Note: Write your answer in terms of the number of days after ticket sales begin.)

tickets=-0.2x^2+12x+11

The number of tickets sold each day for an upcoming performance of Handel's Messiah is given by N(x)=-0.4x^2+9.6x+10, where x is the number of days since the concert was first announced. When will daily ticket sales peak and how many tickets will be sold that day?

To determine the last day that tickets will be sold, we need to find the day when the expected number of ticket sales reaches zero.

The quadratic equation that models the expected number of ticket sales for each day x can be written in the form ax^2 + bx + c = 0. In this case, we can assume that the equation is of the form ax^2 + bx + c = 0, where x represents the number of days after ticket sales begin.

Let's say the quadratic equation is:

f(x) = ax^2 + bx + c

To find the last day when tickets will be sold, we need to find the value of x when f(x) = 0.

Once we have the quadratic equation, we can solve it by factoring, completing the square, or using the quadratic formula.

Let's assume the quadratic equation is f(x) = ax^2 + bx + c = 0.

Step 1: Determine the values of a, b, and c.
Given the quadratic equation, you would need to provide the values of a, b, and c. These values can be obtained by considering the specific information given in the problem or by using historical ticket sales data or other relevant information.

Step 2: Solve the quadratic equation.
Using factoring, completing the square, or the quadratic formula, solve the quadratic equation for x.

Step 3: Determine the last day when tickets will be sold.
After solving the quadratic equation for x, the value(s) obtained will represent the number of days after ticket sales begin. The last day that tickets will be sold will be the highest positive whole number solution for x.

For example, let's say the quadratic equation is f(x) = -2x^2 + 10x + 3 = 0.

We can solve this equation using the quadratic formula:
x = (-b ± √(b^2 - 4ac)) / (2a)

Plugging in the values for a, b, and c from the given equation, we get:
x = (-10 ± √(10^2 - 4(-2)(3))) / (2(-2))
x = (-10 ± √(100 + 24)) / (-4)
x = (-10 ± √124) / (-4)

We can simplify the square root to:
x = (-10 ± 2√31) / (-4)

Now, we can determine the last day when tickets will be sold. Since x represents the number of days after ticket sales begin, we would only consider the positive value of x. In this case, x = (-10 + 2√31) / (-4) = (-5 + √31) / 2.

Therefore, the last day that tickets will be sold is approximately (-5 + √31) / 2 days after ticket sales begin.