Posted by Aria on Monday, August 29, 2011 at 2:58pm.
This is a concept check on quadratic equation application. I am having trouble with a couple of parts. If anyone can help I would appreciate it.
Suppose you are an event coordinator for a large performance theater. You need to supply information about projected ticket sales to the manager. You provide a quadratic equation that models expected number of sales for each day 'x'. (x=1 is the day tickets go on sale."
Tickets=-2x^2+12x+11
I answered a.
B. Describe what happens to the ticket sales as time passes.
I am not sure how to determine this. Do I determine this by the vertex or line of symmetry?
I answered C.
D.Will tickets peak or be at a low during the middle of the sale? How do you know?
Again, this question stumps me. How do you tell something like this with a parabola?
I would appreciate a detailed explanation. I don't want answers as much as how to determine the information.
Thanks for helping.
For D).....
Your parabola should be negative because of the -2X^2. SO the parabola when you graph it is a backwards U. The middle of the backwards "U" has a high maximum so your tickets should be at a peak during the middle of the sale.
As time passes, the ticket sales get higher. Each time you plug in different values of X, the day tickets go on sale, your Y value increases.
Thank you for your help. I understand a whole lot more.
To determine what happens to the ticket sales as time passes, you need to look at the equation and understand its properties. The equation you provided is a quadratic equation in the form Tickets = -2x^2 + 12x + 11, where x represents the number of days since tickets went on sale.
To analyze the behavior of the quadratic equation, you can look at its graph. The graph of a quadratic equation is a parabola, which is a U-shaped curve. In this case, the coefficient of the x^2 term is -2, which means the parabola opens downwards. This indicates that the ticket sales will start high and then decrease over time.
To determine the maximum or minimum point of the parabola, which represents the peak or low point of the ticket sales, you can use the concept of vertex. The vertex of a quadratic function is the point on the graph where it achieves its highest or lowest value. The x-coordinate of the vertex can be found using the formula x = -b / (2a), where a and b are the coefficients of the quadratic equation.
In this case, the quadratic equation Tickets = -2x^2 + 12x + 11 has a = -2 and b = 12. Plugging these values into the formula gives x = -12 / (2*(-2)) = -12 / (-4) = 3. So the x-coordinate of the vertex is 3.
To find the y-coordinate of the vertex, you can substitute the x-coordinate back into the equation. Plugging x = 3 into the equation Tickets = -2x^2 + 12x + 11 gives Tickets = -2*(3^2) + 12*3 + 11 = -2*9 + 36 + 11 = -18 + 36 + 11 = 29. So the y-coordinate of the vertex is 29.
Therefore, the vertex of the parabolic graph is (3, 29). This means that ticket sales will peak on the third day, and the number of tickets sold at that time will be 29.
In summary:
a. As time passes, the ticket sales will decrease since the quadratic equation's graph opens downwards.
b. The vertex of the parabolic graph represents the peak or low point of the ticket sales. The x-coordinate of the vertex can be found using the formula x = -b / (2a), and the y-coordinate can be determined by substituting the x-coordinate back into the equation.
c. Based on the calculation, the ticket sales will peak on the third day (x = 3), and the number of tickets sold will be 29 (y = 29).