A)Use the quadratic equation: Tickets=-0.2^2+12x+11, to determine the last day the that tickets will be sold.(Note: write answer in terms of the number of days after ticket sales begin, x=1 is the day tickets go on sale)

B)Will tickets peak or be at a low during the middle of the sale? How do you know?

I believe that there has to be another part to this question.

I will assume the function describes the number of tickets sold for a given day, if x is the day.

B) the function is a parabola which opens downwards, so it has a max value, the function value being that maximum.

A) The last day when tickets are sold would be the last value of x which is positive (before it crosses the x-axis on its downward path)
so we find the x-intercepts by solving
-0.2^2+12x+11 = 0 (divide by -.2)
x^2 - 60x + 55 = 0
x = (60 ± √(3600 - 4(1)(55))/2
= 59.06 or .93

so it mus be the 59th day.

The first part of the problem says this:

Suppose you are an event coordinator you need to supply information about projected ticket sales to the box office manager, you provide the manager with a quadratic equation that models the expected number of ticket sales for each day x. (x=1, is the day tickets go on sale) tickets=-0.2x^2+12x+11

A) To determine the last day that tickets will be sold based on the quadratic equation given, we need to solve for x when Tickets = 0. Let's rewrite the equation in standard form:

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

Setting Tickets equal to zero, we get:

0 = -0.2x^2 + 12x + 11

To solve for x, we can use the quadratic formula:

x = (-b ± √(b^2 - 4ac)) / (2a)

In our equation, a = -0.2, b = 12, and c = 11.

Plugging in these values, we get:

x = (-(12) ± √((12)^2 - 4(-0.2)(11))) / (2(-0.2))

Simplifying further:

x = (-12 ± √(144 + 8.8)) / (-0.4)

x = (-12 ± √152.8) / (-0.4)

Now, there are two possible outcomes when using the quadratic formula, since we have a ± sign. Let's calculate both possibilities:

x1 = (-12 + √152.8) / (-0.4)

x1 ≈ 29.71

x2 = (-12 - √152.8) / (-0.4)

x2 ≈ -2.96

Since we are looking for the number of days after ticket sales begin, x cannot be negative, so we consider x1 as the valid solution.

Therefore, the last day that tickets will be sold is approximately 30 days after ticket sales begin.

B) To determine whether tickets will peak or be at a low during the middle of the sale, we need to analyze the quadratic equation.

Given the equation Tickets = -0.2x^2 + 12x + 11, the coefficient of x^2 is negative (-0.2). This negative coefficient indicates that the graph of the quadratic equation is an inverted parabola, meaning it opens downwards.

When a quadratic equation opens downwards, the vertex represents the maximum point of the equation. In this case, the vertex represents either the peak or the lowest point of the ticket sales.

To find the x-coordinate of the vertex, we can use the formula:

x = -b / (2a)

In our equation, a = -0.2 and b = 12. Plugging in these values, we get:

x = -(12) / (2(-0.2))

x = -60 / (-0.4)

x = 150

The x-coordinate of the vertex is 150, which corresponds to 150 days after ticket sales begin.

Since the vertex represents the peak or lowest point of the parabola, we can conclude that tickets will peak during the middle of the sale, specifically on day 150.

Therefore, tickets will reach their maximum sales on the 150th day after ticket sales begin.