Question 371028
{{{N(x)= -0.4x^2 +8.8x +15}}}
The easy way to solve this is based on understanding that the graph of N(x) is a parabola. And not only is it a parabola, it is a parabola that opens downward (because of the minus in front of the squared term and because the squared term is x (and not y)).<br<
Once we imagine a picture of a parabola that opens downward, we should realize that the maximum (highest) point will be the vertex of that parabola. So allwe have to do is figure out the vertex.<br>
The quick way to find a vertex is to use {{{x = (-b)/(2a)}}} where the "a" and "b" come from the general equation of quadratic equations: {{{y = ax^2 +bx +c}}}. Using this on N(x) we get:
{{{x = (-8.8)/(2*(-0.4)) = (-8.8)/(-0.8) = 11}}}
So 11 days after the announcement, the ticket sales will be at a peak. And N(11) will tell us how many tickets were sold on that day:
{{{N(11) = -0.4(11)^2 +8.8(11) +15}}}
Simplifying...
{{{N(11) = -0.4(121) +8.8(11) +15}}}
{{{N(11) = -48.4 + 96.8 +15}}}
{{{N(11) = 63.4}}}
So approximately 63 tickets were sold 11 days after the announcement of the concert.