Question 335717
{{{N(x)=-0.4x^2+8.8x+12}}}
Because of the {{{x^2}}} term this is a parabola. And since the coefficient of the {{{x^2}}} term is negative the parabola opens downward. For a downward opening parabola, the maximum value will be at the vertex.<br>
The x coordinate of the vertex for any vertically oriented parabola is {{{(-b)/2a}}}. So the x coordinate of this parabola is:
{{{x = (-b)/2a = (-8.8)/2(-0.4) = (-8.8)/(-0.8) = 11}}}<br>
So the maximum number of tickets will be sold 11 days after the announcement of the concert. The number of tickets sold on that day is:
{{{N(11) = -0.4(11)^2 + 8.8(11) + 12}}}
{{{N(11) = -0.4(121) + 8.8(11) + 12}}}
{{{N(11) = -48.4 + 96.8 + 12}}}
{{{N(11) = 60.4}}}
So there will be approximately 60 tickets sold that day.