Math/Algebra
posted by Angel Eyes on .
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?
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)

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

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.

0.4 x 0.4 = 0.16
8.8 x 8.8 = 77.44
15 x 15 = 225 
to find the roots of 0.4x^2 + 8.8x +15 = 0
I would first "cleanup" 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 
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?

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.

correct

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 :)!

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