The number of tickets sold each day for an upcoming performance of Handel's Messiah is given by N(x)= -0.4x^2 + 8.8x +15, where x is the number of days since the concert was first announced. When will daily ticket sales peak and how many tickets will be sold that day?

Question

Ticket sales will peak ___ days after the concert was first announced.

The number of tickets sold on that day will be ____. (Round to the nearest integer)

Answer 1

find the roots to the quadratic. Maximum will be halfway between the roots.

Answer 2

That's where I got lost was when I was trying to find the roots of the quadratic equation. I guess I just need more practice with these roots.

Answer 3

0.4 x 0.4 = 0.16
8.8 x 8.8 = 77.44
15 x 15 = 225

Answer 4

to find the roots of -0.4x^2 + 8.8x +15 = 0
I would first "clean-up" the equation. I don't like decimals in my equations so I would multiply each term by 10
-4x^2 + 88x + 150 = 0
divide by -2
2x^2 - 44x - 75 = 0
a=2, b=-44, c=-75
x = (-b ± √(b^2 - 4ac))/(2a)
= (44 ± √2536)/4
= 23.5897 and -1.58987

the halfway value of x, as bobpursely suggested, is 11
so N(11) = -.4(121) + 8.8(11) + 15 = 63.4

another way is to know that for any function
f(x) = ax^2 + bx + c, the max/min occurs when
x = -b/(2a)

then -b/(2a) = -8.8/(2(-.4)) = 11 as above

Answer 5

So then I would end up with the ticket sales would peak 11 days after, and the number of tickets sold that day would be 63.4 Correct or No?

Answer 6

Although it says to round to the nearest integer. So this would actually be sales peak 11 days after, and the number of tickets sold would just be 63.

Answer 7

correct

Answer 8

Ahhhh Thank you very much! I seem to get lost when it comes to the cleaning up the decimals & then trying to get the square root if it is in decimal form. I appreciate your help Reiny :)!

Answer 9

The number of tickets sold each day for an upcoming Handel’s Messiah is given by N(x)=-0.5x^2+12x+15