The number of tickets sold each day for an upcoming performance is given by N(x)=-0.3x^2+9x+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?

Answer 1

for any quadratic function
f(x) = ax^2 + bx + c
the x of the vertex is -b/(2a)
sub that x value into the function to get the y of the vertex, so

n(x) = -.3x^2 + 9x + 15
x of vertex is -9/(2(-.3)) = 15
n(15 = -.3(225) + 9(15) + 15
= 82.5

ticket sales will peak on day 15 and they will sell 83 tickets, ( can't sell partial tickets)

check for reasonableness of answer
let x = 14
n(14) -.3(196) + 9(14) + 15 = 82.2 , < 82.5
let x = 16
n(16) = -.3(256) + 9(16) + 15 = 82.2 , < 82.5

I'll go with my answer