Question 622269
this question involves something called completing the square.

so first take your equation, {{{y=-0.4x^2+9.6+12}}}
factor out the -0.4 from terms ax + bx and you will get, 

{{{y=-0.4(x^2-24x)+12}}}
now divide -24 by two and square it. you will get 144. add then subtract 144, as this wont change the equation.

now we have:

{{{y=-0.4(x^2-24x+144-144)+12}}}
now multiply -0.4 by (-144) and move it outside the bracket so you get:

{{{y=-0.4(x^2-24x+144)+12+57.6}}}
now the stuff inside the bracket is a perfect sqaure as {{{(x^2-24x+144)=(x-12)^2}}}
so now we have,

{{{y=-0.4(x-12)^2+69.6}}}
now since we are looking ffor the vertex, we have at 12 days, 70 tickets are sold.

NOTE: you can complete the square for any standard form quadratic, unlike factoring.
NOW if you know calculus this makes it much easier as all you need to do is take the derivative and set it to zero, as you will get 
{{{y=-0.4x^2+9.6x+12}}}
 {{{ y = -0.8x + 9.6 = 0 }}}  {{{x=12}}}
plug it into the initial equation, {{{y=-0.4(12)^2+9.6(12)+12}}} ---> {{{y=69.6}}}