Question 329394
The minus sign in front of the {{{x^2}}} term tells me
that the curve has a max at the top, not a min at the
bottom. What is needed is to find the point MAX(x,N)
For an equation of the form {{{y = a*x^2 + b*x + c}}},
{{{x[max]}}} is at {{{-b/(2a)}}}. For the given equation:
{{{N(x) = -.3x^2 + 6x + 10}}}
{{{b = 6}}}
{{{a = -.3}}}, so
{{{x[max] = -6/(2*(-.3))}}}
{{{x[max] = 10}}}
Now I need to find {{{N[max]}}}
{{{N(x) = -.3x^2 + 6x + 10}}}
{{{N[max] = -.3*100 + 6*10 + 10}}}
{{{N[max] = -30 + 60 + 10}}}
{{{N[max] = 40}}}
Ticket sales will peak on the 10th day and 40 tickets will be sold that day
Here's a graph of equation:
{{{ graph( 500, 500, -1, 20, -5, 50,  -.3x^2 + 6x + 10) }}}