Question 466765
Since this is a quadratic function, its graph is parabolic.
The leading coefficient(-0.4) is negative, this tells us its a downward pointing parabola.
The vertex of this parabola will give us the maximum value of N(x) or the highest daily ticket sales and the day it occurred.
To find vertex, first find line of symmetry or x_coordinate of vertex.
{{{x = (-b)/2a}}}
where
a = -0.4
b = 12
c = 12
{{{x = (-12)/2(-0.4)}}}
{{{x = 15}}}
Substitute this value into function
{{{y = -0.4(15^2) + 12(15) + 12}}}
{{{y = -90 + 180 + 12}}}
{{{y = 102}}}
Vertex: (15,102)
Thus, on the 15th day ticket sales peaked at 102 tickets sold.