x=1 is the day tickets go on sale.

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

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

MY ANSWER: 60 days

Stuck on this portion:
will tickets peak or be at a low during the middle of the sale and how do you know?

To determine if the tickets will peak or be at a low during the middle of the sale, we need to analyze the behavior of the quadratic equation. The given equation for the number of tickets sold is Tickets = -0.2x^2 + 12x + 11, where x represents the number of days since ticket sales began.

To find out if the tickets will peak or be at a low during the middle of the sale, we need to look at the shape of the graph of this equation.

The equation is in the form of a quadratic function: y = ax^2 + bx + c. In this case, a = -0.2, b = 12, and c = 11. The coefficient 'a' tells us whether the graph opens upwards or downwards.

If 'a' is positive, the graph opens upwards, and the ticket sales will peak during the middle of the sale. Conversely, if 'a' is negative, the graph opens downwards, and the ticket sales will be at a low during the middle of the sale.

In our equation, a = -0.2, which is negative. Therefore, the graph will open downwards, suggesting that the ticket sales will be at a low during the middle of the sale.

To confirm this visually, you can plot the graph. Using graphing software or an online graphing calculator, plot the equation Tickets = -0.2x^2 + 12x + 11. You will see that the resulting graph is a downward-facing parabola, indicating that ticket sales will be at a low during the middle of the sale.

However, to determine when this low point occurs, we can calculate the x-coordinate of the vertex of the parabola. The vertex is the highest or lowest point on the graph, and it represents the middle or turning point of the quadratic function.

The x-coordinate of the vertex in a quadratic function of the form y = ax^2 + bx + c can be calculated using the formula x = -b / (2a). In this case, a = -0.2 and b = 12. Plugging these values into the formula, we have:

x = -12 / (2 * (-0.2))
x = -12 / (-0.4)
x = 30

So, the lowest point of ticket sales during the middle of the sale occurs at 30 days after ticket sales begin.

Therefore, based on the analysis of the equation and the graph, we can conclude that the tickets will be at a low point during the middle of the sale at 30 days after ticket sales begin.