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.

Question

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.

Answer 1

B. The direction of the parabola, which is downwards because of the -2x^2 term, will tell you that the ticket sales will decrease as x increases.
e.g. if x = 2 , Sales = -8 + 24 + 11 = 27
if x = 3, sales = -18 + 36 + 11 = 29
if x = 4, sales = -32 + 48 + 11 = 27
if x = 5 , sales = -50 + 60+11 = 21 , notice the sales are decreasing
it also looks like the vertex is at (3,29)
( Assume you know how to find the vertex)

so as x gets bigger (time passes), the first term becomes more negative at a faster rate than the two positive terms, so the sum (the ticket sales) gets smaller, until it becomes meaningless when ticket sales is a negative number.
(e.g. x = 10, sales = -200 + 120 + 11 = -69 )

I suggest you sketch the relation after making a table of values for x = 1,2,3,4,5,6,7

However keep in mind that you don't have a continuous curve, but rather a series of integer valued points, which will fall along the parabola
The vertex of (3,29) tells you that there was a maximum number of ticket sales of 29 on day 3
notice when x=6, sales = -72 + 72 + 11 = 11
but when x-7, the graph no longer has any real meaning.

Answer 2

Thanks a bunch. I appreciate the detail. quadratic equations are confusing for me to graph. I no sooner think I have it than I get an answer wrong.