Question

(x=1 is the day tickets go on sale)

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

1) 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.

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

For this problem I already solved for the peak value that will occur on day 30 by using the formula -b/(2a).

When x is 30 the maximum value of y is 191. right?

To find the last day the tickets could be on sale I need to factor to find the two values in which the value of x is 0. (or use the quadratic formula) I'm not sure I did this right because it doesn't look right. can someone help and verify if I am on the right track?

Answer 1

-0.2x^2+12x+11

When x = 30, y = 191, so yes, you are correct.

Solve this equation by completing the square,
-0.2x^2+12x+11
Divide both sides by -0.2
x^2 - 60x - 55 = 0
x^2 - 60x = 55
x^2 - 60x + 900 = 55 + 900
(x - 30)^2 = 955
+ - (x - 30) = (sqrt(955))

+ x - 30 = 30.9031
x = 60.9031

- x + 30 = 30.9031
- x = 0.9031
x = -0.9031