SOLUTION: the number of tickets sold each day for an upcoming performance is given by N9x) = -0.4x^2 + 9.6x + 12, where x is the number of days since the concert was first announced. When wi

Algebra ->  Quadratic Equations and Parabolas -> SOLUTION: the number of tickets sold each day for an upcoming performance is given by N9x) = -0.4x^2 + 9.6x + 12, where x is the number of days since the concert was first announced. When wi      Log On


   

Question 622269: the number of tickets sold each day for an upcoming performance is given by N9x) = -0.4x^2 + 9.6x + 12, where x is the number of days since the concert was first announced. When will daily tickets peak and how many tickets will be sold that day?
Answer by matineesuxxx(27) About Me  (Show Source):
You can put this solution on YOUR website!
this question involves something called completing the square.
so first take your equation, y=-0.4x%5E2%2B9.6%2B12
factor out the -0.4 from terms ax + bx and you will get,
y=-0.4%28x%5E2-24x%29%2B12
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%28x%5E2-24x%2B144-144%29%2B12
now multiply -0.4 by (-144) and move it outside the bracket so you get:
y=-0.4%28x%5E2-24x%2B144%29%2B12%2B57.6
now the stuff inside the bracket is a perfect sqaure as %28x%5E2-24x%2B144%29=%28x-12%29%5E2
so now we have,
y=-0.4%28x-12%29%5E2%2B69.6
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%5E2%2B9.6x%2B12
+y+=+-0.8x+%2B+9.6+=+0+ x=12
plug it into the initial equation, y=-0.4%2812%29%5E2%2B9.6%2812%29%2B12 ---> y=69.6