Need help with this N(x) = -0.4x^2 + 11.2x + 12 -- Will give best answer

The number of tickets sold each day for an upcoming performance of Handel's Messiah is given by N(x) = -0.4x^2 + 11.2x + 12, 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?

N(x) = -0.4x^2 + 11.2x + 12

Find the derivative:

N'(x) = -0.8x + 11.2

Find x-values where this equals 0:

-0.8x + 11.2 = 0

0.8x = 11.2

x = 14

So, on day 14 ticket sales will peak. Plug this back into the original equation to see what sales will be that day:

N(14) = -0.4(14)^2 + 11.2(14) + 12
N(14) = -78.4 + 156.8 + 12
N(14) = 90.4

So, on day 14 when ticket sales are at the highest, they will sell about 90 or 91 tickets.

N(x) = -0.4x² + 11.2x + 12

is a parabola that opens downward and its peak occurs at the axis of symmetry:

x = -b/2a = -11.2/2(-0.4) = 14

This mean that the peak occurs on the 14th day after announcement.

The number of tickets sold will be:

N(14) = -0.4(14)² + 11.2(14) + 12 = 90.4

i find it easiest to use part of the quadratic equation for this; specifically the -b/2a part

so you have x= -b/2a
x = -11.2 / 0.8
x = 14

now just sub in your x value and solve for N(x) !

so N(14) = -0.4(14^2) + 11.2(14) + 12 = 90.4 tickets!